Dual Mesh Research Articles

Ultrashort-term dual ultraviolet-irradiated nickel-doped titanium dioxide nanoparticle mesh for photocatalytic disinfection with minimum exposure risk to human health

The photocatalytic antibacterial activity of a nickel-doped titanium dioxide nanoparticle mesh (Ni–TiO 2 mesh) against E. coli was investigated in chlorinated water under ultrashort-term dual ultraviolet (UV) irradiation. Ni–TiO 2 nanoparticles (NPs) were prepared via Ni doping to TiO 2 NPs and uniformly distributed on the mesh via electrospraying and hot-pressing, of which the morphology and particle size distribution were maintained after immobilization. In the Ni–TiO 2 mesh, the elements, Ti, O, Ni, iron, chromium and silicon were included suggesting multi- and mixed metal oxides. Irradiation distance and lamp cleaning were analyzed as controllable factors to maintain the dual UV intensity. The Ni–TiO 2 mesh showed a significant antibacterial activity even at the smallest mesh size of 0.25 cm 2 under 5-sec irradiation after the UV intensity adjustment. The results suggest that the improved NP characteristics on a steel mesh substrate, including multi- and mixed metal oxides, can display photocatalytic antibacterial activity against E. coli along with minimization of NP exposure due to NP immobilization. This can be directly extended to other environmental, industrial, and clinical applications as a safe and sustainable photocatalytic antibiotic agent for photocatalytic disinfection. • Dual UV-irradiated Ni-TiO 2 mesh was developed as a next-generation photocatalytic antibiotic agent for disinfection. • Free Ni-TiO 2 NPs were immobilized on the steel mesh via electrospraying and hot-pressing for improved characteristics. • Under ultrashort-term dual UV irradiation, the Ni-TiO 2 mesh had a significant antibacterial activity against Escherichia coli in chlorinated water, compared to UV alone. • The Ni-TiO 2 mesh can be promisingly extended to combined disinfection for enhanced antibiotic performance under ultrashort-term dual UV irradiation.

A novel numerical method for the solution of nonlinear equations with applications to heat transfer

PurposeThe purpose of this study is to extend a novel numerical method proposed by the first author, known as the dual mesh control domain method (DMCDM), for the solution of linear differential equations to the solution of nonlinear heat transfer and like problems in one and two dimensions.Design/methodology/approachIn the DMCDM, a mesh of finite elements is used for the approximation of the variables and another mesh of control domains for the satisfaction of the governing equation. Both meshes fully cover the domain but the nodes of the finite element mesh are inside the mesh of control domains. The salient feature of the DMCDM is that the concept of duality (i.e. cause and effect) is used to impose boundary conditions. The method possesses some desirable attributes of the finite element method (FEM) and the finite volume method (FVM).FindingsNumerical results show that he DMCDM is more accurate than the FVM for the same meshes used. Also, the DMCDM does not require the use of any ad hoc approaches that are routinely used in the FVM.Originality/valueTo the best of the authors’ knowledge, the idea presented in this work is original and novel that exploits the best features of the best competing methods (FEM and FVM). The concept of duality is used to apply gradient and mixed boundary conditions that FVM and its variant do not.

Single Center Observational Study to Evaluate the Safety and Efficacy of Self-expanding Composite Mesh for Repair of Small Umbilical Hernias

Background: There is evidence that mesh repair for umbilical hernias results in fewer recurrences. Early and late complication rates of mesh repair are variable with different techniques of mesh repair. In recent years, several mesh device for the repair of small ventral hernias have been developed, but some reports have been published reporting some adverse outcomes like high recurrences or wound related complications encountered with those mesh devices. The purpose of this study was to evaluate the safety and efficacy of small umbilical hernia(<3cm) repair using self expanding dual mesh.
 Methods: In this study we used a composite self-expanding mesh with Polypropylene(PP) on one side and expanded polytetrafleuroethylene(ePTFE) on the other side. We introduced this technique in our department at BIRDEM General Hospital and IMC in March 2017 and collected patients data and outcome in an observational study of 25 consecutive patients matching our inclusion criteria until February 2019. In addition to the routine 1st week postoperative follow-up, We did a prospective follow-up at 1 month,6 month and 1 year which included a questionnaire, clinical examination and ultra sonogram after 12 months.
 Results: The study included 15 female and 10 male patients with age ranging from 25-62 years(Mean- 47) having 16 primary umbilical hernia and 9 umbilical port hernias. The size of gap was <3cm and all except 2 hernias were reducible. In all patients a self expanding dual mesh was used with a diameter of 8cm(18 patients) or 6.4(7 patients) cm. Early complications included superficial wound infection-1(4%), seroma-1(4%), serosanguinous discharge-1(4%) and ecchymosis-1(4%). No major wound problems were noted in 1 month or 6 month follow-up except 1 patient reporting hypertrophied scar. At 1st month follow up 21 patientswere pain free, after 6 month only 1 patient reported mild pain, after 1 year 100% patients were pain free. 24 out of 25 patients ie 96% were very satisfied with the result of their repair. There was no recurrence after one year.
 Conclusion: Umbilical and umbilical port hernia repair with Self expanding dual mesh is effective and is cosmetically very appreciated by patients as good as laparoscopic repair. Therefore, we recommend using these meshes only for umbilical and umbilical port hernias smaller than 3 cm. For larger or incisional hernias other techniques allowing the use of larger meshes is advocated.
 Journal of Surgical Sciences (2020) Vol. 24 (2) : 43-50

Finite volume arbitrary Lagrangian-Eulerian schemes using dual meshes for ocean wave applications

For reasons of efficiency and accuracy, water wave propagation is often simulated with potential or inviscid models rather than Navier-Stokes solvers, but for wave-induced flows, such as wave-structure interaction, viscous effects are important under certain conditions. Alternatively, general purpose Navier-Stokes (CFD) models can have limitations when applied to such free-surface problems when dealing with large amplitude waves, run-up, or propagation over long distances. Here we present an Arbitrary Lagrangian-Eulerian (ALE) algorithm with special care to the time-stepping and boundary conditions used for the free-surfaces, integrated into Code_Saturne, and we test its capabilities for modeling a variety of water wave generation and propagation benchmarks, and finally consider interaction with a vertical cylinder. Two variants of the mesh displacement computation are proposed and tested against the discrete Geometric Conservation Law (GCL). The more robust variant, for highly curved or sawtoothed free-surfaces, uses a Compatible Discrete Operator scheme on the dual mesh for solving the mesh displacement, which makes the algorithm valid for any polyhedral mesh. Results for standard wave propagation benchmarks for both variants show that, when care is taken to avoid grids with excessive numerical dissipation, this approach is effective at reproducing wave profiles as well as forces on bodies.

A prospective randomized trial comparing Restorelle® Y mesh and flat mesh for laparoscopic and robotic-assisted laparoscopic sacrocolpopexy: 24-month outcomes.

To compare prolapse recurrence and the incidence of mesh exposure between Restorelle® Y mesh and dual flat mesh. A randomized trial of women undergoing laparoscopic (LSC) or robotic (RSC) sacrocolpopexy for post-hysterectomy vaginal prolapse. Subjects were randomized to either Y mesh or dual flat mesh. Subjects underwent a pelvic examination with POP-Q and evaluation of any mesh exposure, and the PFDI-20 was administered at 6, 12 and 24months postoperatively. Subjective recurrence was defined by symptomatic vaginal bulge. All subjects underwent pelvic examination with POP-Q at 6, 12 and 24months. Objective recurrence was defined by descent of the apex > 1/3 into the vaginal canal, anterior or posterior vaginal descent beyond the hymen, or retreatment for prolapse. Sixty-two patients were enrolled, and 59 patients were implanted with mesh: 30 Y mesh (17 LSC, 13 RSC) and 29 flat mesh (18 LSC, 11 RSC). There were no differences in patient characteristics between the groups. At 24months, data were available for 44 (74.5%) patients. There were no mesh exposures for all subjects. PFDI-20 scores improved significantly for all subjects with no differences in mean improvement by mesh configuration. There were no differences in subjective and objective recurrence rates between the groups. Four patients (9.1%) complained of subjective vaginal bulge symptoms while nine (20.5%) patients had an objective recurrence (77.8% [7] examination only and 22.2% [2] reoperation). There were no apical recurrences. Of those patients who had a recurrence on examination only (n = 7), 85.7% (6) were asymptomatic. At 24months, there were no differences in subjective outcomes and prolapse recurrence in patients who underwent sacrocolpopexy with the Restorelle® Y mesh versus dual flat mesh. One in five patients experienced an objective recurrence; however, there were no apical recurrences and the majority were asymptomatic.

A new Hodge operator in discrete exterior calculus. Application to fluid mechanics

<p style='text-indent:20px;'>This article introduces a new and general construction of discrete Hodge operator in the context of Discrete Exterior Calculus (DEC). This discrete Hodge operator permits to circumvent the well-centeredness limitation on the mesh with the popular diagonal Hodge. It allows a dual mesh based on any interior point, such as the incenter or the barycenter. It opens the way towards mesh-optimized discrete Hodge operators. In the particular case of a well-centered triangulation, it reduces to the diagonal Hodge if the dual mesh is circumcentric. Based on an analytical development, this discrete Hodge does not make use of Whitney forms, and is exact on piecewise constant forms, whichever interior point is chosen for the construction of the dual mesh. Numerical tests oriented to the resolution of fluid mechanics problems and thermal transfer are carried out. Convergence on various types of mesh is investigated. Flat and non-flat domains are considered.

A Single-Layer Dual-Mesh Boundary Element Method for Multiscale Electromagnetic Modeling of Penetrable Objects in Layered Media

A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM formulations either lead to a poorly conditioned system matrix for multiscale problems, or are computationally expensive for objects embedded in layered substrates. This article presents a new BEM formulation which leverages the surface equivalence principle and Buffa-Christiansen basis functions defined on a dual mesh, to obtain a well-conditioned system matrix suitable for multiscale EM modeling. Unlike existing methods involving dual meshes, the proposed formulation avoids the double-layer potential operator for the surrounding medium, which may be a stratified substrate requiring the use of an advanced Green's function. This feature greatly alleviates the computational expense associated with the use of Buffa-Christiansen functions. Numerical examples drawn from several applications, including remote sensing, chip-level EM analysis, and metasurface modeling, demonstrate speed-ups ranging from 3x to 7x compared to state-of-the-art formulations.

Clinical Outcomes of Ventral Hernia Repair with Ventralex Patch- A Retrospective Study from a Tertiary Care Centre

Introduction: There are several described techniques for ventral hernia mesh repair in both laparoscopic and open approach. Both approaches have their own pros and cons. Ventralex patch repair is an open technique using dual mesh in the intraperitoneal plane for ventral hernia repair. Aim: To describe an open technique with the use of ventalex patch in the repair of selected ventral hernias and to compare the open technique in terms of cost, operating time, complications and duration of hospital stay with the similar studies using Ventral patch and available literature for open and laparoscopic repair. Materials and Methods: This retrospective study was conducted on 248 patients over a period of seven years who underwent open ventral hernia repair with the Ventralex Patch, at a tertiary care hospital. A retrospective chart review and telephonic interview was conducted postoperatively and at the end of at least 24 months to assess for outcomes, particularly recurrence. Descriptive statistics reported using frequency and percentage for categorical variables. Continuous variables were reported using mean±Standard Deviation (SD). Results: A total of 248 patients underwent hernioplasty with ventralex patch. The mean age was 50.57 years and mean BMI was 28.37 kg/m2. The average duration of operation was 27.5 minutes and hospital stay was 2.275 days. The most common defect size was 2 cm (47.2%). The cost analysis of this technique revealed an average cost of INR 35,142 as opposed to an average cost of INR 88,601 for laparoscopic repair (including disposables) and INR 30,174 for open traditional sub-lay repair. Twenty-one patients developed surgical site infection (8.5%), and 27 patients (10.9%) developed seroma formation. A total of six patients developed superficial skin necrosis. The cumulative hernia recurrence rate at the end of 24 months was 6.5% (16/248). Conclusion: Ventralex patch repair is very efficient and effective in the treatment of selective umbilical, periumbilical, epigastric and incisional hernias with a comparable complication profile in terms of short term complications and recurrence rate compared to available literature.

Bilayer Mesh Repair for Inguinal Hernia- The Open Alternative to Laparoscopic Repairs

Introduction: In 1999, Gilbert described the technique of using a bilayer mesh device, Prolene Hernia System (PHS) for tension free repairs of inguinal hernias through an open anterior approach. This provides an anterior, posterior and plug repair, and hence successfully covers the myopectineal orifice, the lack of which is a glaring drawback for the Lichtensteins repair. This also confers the same benefit provided by the laparoscopic hernia repairs which uses the preperitoneal space to cover this same region that is, Transabdominal Preperitoneal Patch Plasty (TAPP) and Total Extraperitoneal patch Plasty (TEP). Aim: To observe the overall outcome of using the open bi-layered dual mesh in a population of Odisha, attending a tertiary care hospital. Materials and Methods: All patients admitted with inguinal hernias in the Department of General Surgery, Pradyumna Bal Memorial Hospital, KIMS, Odisha, India were included in the study. They all underwent the PHS bilayer mesh repair. The relevant patient specifics like, preoperative clinical findings and intra and postoperative results were noted in a master chart. Patients were followed-up for one year, and further long-term complications were noted, if any. Results: There were a total of 40 patients. The mean duration for the procedure was 61 minutes (SD-22.8) and there was no inadvertent injury. The patients were encouraged to resume all physical activities from the first postoperative day. All the patients had an uneventful recovery, with a mean hospital stay of four days. Four patients presented with seroma after one week of surgery, while 22 patients had cord oedema. Both subsided spontaneously within three weeks, without further intervention. No recurrence was noted in any of the patients. Conclusion: The PHS bilayer dual mesh repair is ideally suited for population in a low resource setting. It ensures coverage of the entire vulnerable area of groin along with a considerably shorter duration of operation, minimal risk of intraoperative injury.

New superconvergent structures developed from the finite volume element method in 1D

New superconvergence structures are introduced by the finite volume element method (FVEM), which gives us the freedom to choose the superconvergent points of the derivative (for odd order schemes) and the superconvergent points of the function value (for even order schemes) for $k\geq 3$. The general orthogonal condition and the modified M-decomposition (MMD) technique are established to prove the superconvergence properties of the new structures. In addition, the relationships between the orthogonal condition and the convergence properties for the FVE schemes are carried out in Table 1. The above results are also valid to $k=1,2$. For these cases, the new superconvergence structures are the same with the Gauss-Lobatto structure, which yields to the FVE schemes with Gauss-points-dependent dual meshes. Numerical results are given to illustrate the theoretical results.

Conforming weighted delaunay triangulations

Given a set of points together with a set of simplices we show how to compute weights associated with the points such that the weighted Delaunay triangulation of the point set contains the simplices, if possible. For a given triangulated surface, this process provides a tetrahedral mesh conforming to the triangulation, i.e. solves the problem of meshing the triangulated surface without inserting additional vertices. The restriction to weighted Delaunay triangulations ensures that the orthogonal dual mesh is embedded, facilitating common geometry processing tasks. We show that the existence of a single simplex in a weighted Delaunay triangulation for given vertices amounts to a set of linear inequalities, one for each vertex. This means that the number of inequalities for a given triangle mesh is quadratic in the number of mesh elements, making the naive approach impractical. We devise an algorithm that incrementally selects a small subset of inequalities, repeatedly updating the weights, until the weighted Delaunay triangulation contains all constrained simplices or the problem becomes infeasible. Applying this algorithm to a range of triangle meshes commonly used graphics demonstrates that many of them admit a conforming weighted Delaunay triangulation, in contrast to conforming or constrained Delaunay that require additional vertices to split the input primitives.

Comparison of subpectoral versus dual-plane implant based immediate breast reconstruction after nipple-areola sparing mastectomy

Selection of implant pocket and size is a dilemma for surgeons especially if radiation therapy is envisaged after implant based immediate breast reconstruction (IBR). The aim of this study is to compare complication rates between subpectoral and the dual plane polyglactin mesh supported IBR after nipple-areola sparing mastectomy. Reconstructive analysis of 208 breasts of 190 patients with breast cancer undergoing implant based IBR at a single university hospital were evaluated. The patients were reconstructed with either dual-plane polyglactin mesh supported (n=91) or subpectoral (n=117) implant based IBR after nipple-areola sparing mastectomy. Demographic data, and postoperative complications were compared. The mean age was 43.3 years. Early complications encountered in 12% (n=25) and late complications occurred in 18% (n=37) of breasts. Both early (13,7% vs 9.9%, P=0.406) and late complications (24.8% vs 8.8%, P=0.003) were more common in subpectoral group, but only late complication occurrence rate was statistically significant. Capsular contracture (P=0.000), inframammary fold problems (P=0.010), bottoming-out (P=0.370), mechanical shift (P=0.036) and animation deformity (P=0.007) were all more common in subpectoral group. Only rippling deformity (P=0.011) was more common in dual plane group. Dual plane IBR has acceptable complication rates compared to subpectoral IBR. It is associated with less capsular contracture, fewer animation and bottoming-out deformity and better inframammary fold appearance.

A discrete nonlocal damage mechanics approach

In this paper the authors develop the governing equations for a finite element model of micro-cracking based on a novel approach, eschewing differential equations and continuum mechanics. Instead of first stating the continuum balance laws and constitutive relations followed by discretization, the body is discretized first and then the equations of equilibrium are directly stated for the discretized body. It is shown that, as a result, the balance laws and constitutive relations can be entirely stated in terms of edge forces and lengths rather than strains. Furthermore, by ensuring that microcracks always propagate along the dual mesh which represents the possible fracture microplanes in the element, the need for creating additional nodes, gap elements or cohesive zones is avoided. Finally, the notion of the survival probability of a fracture microplane is introduced and the transition probability evolution is described by using probabilistic notions from population models. Thus the resulting governing equations can be solved by a conventional elastic predictor, followed by a nonlocal fracture corrector, making this convenient to augment conventional elements with fracture abilities.

One-month results from a prospective experience on CAS using C-GUARD stent system: the IRONGUARD-2 study

Abstract Objectives To evaluate 30-day safety and efficacy of dual layered mesh covered carotid stent systems (DLS) for carotid artery stenting (CAS) in the clinical practice. Background When compared to carotid endarterectomy CAS has been associated to an higher rate of post procedural neurologic events; these could be related to plaque's debris prolapsing through stent's mesh. Consequently, the need for increased plaque coverage has resulted in the development of DLS. Methods From January 2017 to June 2019 a physician-initiated, prospective, multispecialty, registry enrolled 733 consecutive patients undergoing CAS using the CGuard Embolic Prevention System (EPS) in 20 centres. Primary endpoint was the stroke up to 30 days; secondary endpoints were the technical and procedural success; external carotid artery (ECA) occlusion; in-hospital and 30 days transient ischemic attack (TIA), acute myocardial infarction (AMI) and death rates. Results Symptoms were present in 131 patients (17.87%). An embolic protection device (EPD) was used in 731 patients (99.72%). Procedural success was 100%, technical success was obtained in all but one patient (99.86%), who died in-hospital due to a haemorrhagic stroke. Six TIAs, 2 minor strokes, and 1 AMI occurred during in-hospital stay, ECA occlusion was evident in 8 patients (1.09%). Between hospital discharge and 30-day, 2 TIAs, 1 minor stroke and 3 AMIs occurred. Therefore, the stroke rate at 30 days was 0.13. Conclusion This real-world registry suggests that use of CGuard EPS in clinical practice is safe and associated to a minimal occurrence of adverse neurological events up to 30 days follow up. Funding Acknowledgement Type of funding source: None

Use of dual layered stents in endovascular treatment of extracranial stenosis of the internal carotid artery: one year results of a patient-based meta-analysis of 4 clinical studies

Abstract Background Small sized clinical studies evaluating one year outcomes of CAS performed with two available DLS, Roadsaver® (RS) and CGuard® (CG), have been published. Purpose To evaluate one year safety and efficacy of dual layered mesh covered carotid stent systems (DLS) for carotid artery stenting (CAS). Methods We performed an individual patient-level meta-analysis including studies enrolling more than 100 CAS with DLS. Primary endpoint was the death and stroke rate; secondary endpoints were restenosis and in-stent thrombosis rates at one year. Results Patients were divided in two groups according to DLS (RS N=250; CG N=306). At one year, 11 patients died (1.97%), 7 patients in the group RS (2.8%) and 4 patients in the CG one (1.31%), 10 strokes occurred, 4 in the group RS (1.6%) and 6 in the CG one (1.96%). Overall death and stroke rate was 3.77% (N=21), 11 events in the group RS (4.4%) and 10 in the CG group (3.27%). Symptomatic status was the only predictor of death and or stroke. At one year restenosis occurred in 12 patients (2.1%), 10 in the group RS (4%) and 2 in the CG one (0.65%) (p=0.007). In stent thrombosis occurred in 1 patient (0.18%) of the group CG (0.32%). RS use was the only independent restenosis predictor. Conclusions This study suggests that DLS use for CAS is associated to a low one year death and stroke rate and specific DLS stent use could affect restenosis rate. Funding Acknowledgement Type of funding source: None

3D finite-volume time-domain modeling of geophysical electromagnetic data on unstructured grids using potentials

Unstructured grids are capable of faithfully representing real-life geologic models and topography with relatively few mesh cells. We have developed a finite-volume solution to the 3D time-domain electromagnetic forward modeling problems using unstructured Delaunay-Voronoï dual meshes. We consider the Helmholtz equation for the electric field and a combination of the Helmholtz equation and the conservation of charge equation for the magnetic vector (A) and electric scalar ([Formula: see text]) potentials. The [Formula: see text] formulation requires initial values for A that can be obtained by solving the magnetostatic problem. We use backward Euler time stepping to advance the electric field and the potentials in the time domain. When using the potential method, the electric and magnetic fields are calculated from [Formula: see text] solutions. To obtain consistent potential solutions at different time steps, we enforce the Coulomb gauge condition, using implicit and explicit methods. We validate the proposed method with a simple 3D conductive block model and with a comparison with other numerical methods. By using [Formula: see text] potentials, it is possible to decompose the electric field into galvanic and inductive parts, which is helpful in understanding the physics behind the behavior of the electromagnetic fields in the ground. We use vector plots to visualize the decomposed electric fields for horizontal and vertical thin conductor models with inductive loop sources. This allows the interplay between inductive and galvanic parts as the electric field and current density develop with time to be visualized.

Dual mesh control domain analysis of functionally graded circular plates accounting for moderate rotations

Nonlinear analysis of the axisymmetric bending of circular plates, accounting for through-thickness power-law variation of a two-constituent material and the von Kármán nonlinearity is presented using the dual mesh control domain methods (DMCDM). The classical and first-order shear deformation theory kinematics are used and displacement and mixed models are developed using the DMCDM. The DMCDM predicts displacements as accurate as the finite element method (FEM), but has the advantage of predicting the stress resultants more accurately than the FEM. The developed computational models are used to determine the effect of the geometric nonlinearity and power-law index on the bending deflections and stress resultants of functionally graded circular and annular plates with different boundary conditions. It is found that the power-law index, which dictates the material distribution through the thickness, has two different regions of response, one with steep increase in deflections followed by relatively slow increase with respect to the power-law index.

A dual mesh finite domain method for steady-state convection–diffusion problems

The dual-mesh finite domain method (DMFDM) proposed by Reddy (2019)[1] is used to study the steady-state convection–diffusion problems in 1D and 2D. In the DMFDM, one mesh of finite elements for the approximation of the domain and primary variables and another mesh of control domains, which also covers the whole domain, to satisfy the governing differential equations are used. The approach is distinguished from both the finite element method and the finite volume method, although the method shares the desirable features of both methods. Numerical examples are presented to illustrate the methodology and accuracy compared to the finite element and finite volume solutions.

A Novel Staggered Semi-implicit Space-Time Discontinuous Galerkin Method for the Incompressible Navier-Stokes Equations

A new high order accurate staggered semi-implicit space-time discontinuous Galerkin (DG) method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions. The staggered DG scheme defines the discrete pressure on the primal triangular mesh, while the discrete velocity is defined on a staggered edge-based dual quadrilateral mesh. In this paper, a new pair of equal-order-interpolation velocity-pressure finite elements is proposed. On the primary triangular mesh (the pressure elements) the basis functions are piecewise polynomials of degree $N$ and are allowed to jump on the boundaries of each triangle. On the dual mesh instead (the velocity elements), the basis functions consist in the union of piecewise polynomials of degree $N$ on the two subtriangles that compose each quadrilateral and are allowed to jump only on the dual element boundaries, while they are continuous inside. In other words, the basis functions on the dual mesh are built by continuous finite elements on the subtriangles. This choice allows the construction of an efficient, quadrature-free and memory saving algorithm. In our coupled space-time pressure correction formulation for the incompressible Navier-Stokes equations, arbitrary high order of accuracy in time is achieved through the use of time-dependent test and basis functions, in combination with simple and efficient Picard iterations. Several numerical tests on classical benchmarks confirm that the proposed method outperforms existing staggered semi-implicit space-time DG schemes, not only from a computer memory point of view, but also concerning the computational time.

A high order conservative flux optimization finite element method for steady convection-diffusion equations

This article presents a high order conservative flux optimization (CFO) finite element method that preserve the important mass conservation property locally for the convection-diffusion equations. The numerical scheme is an extension of the first order CFO scheme proposed in [25], it is based on the classical Galerkin finite element method enhanced by a flux approximation on the boundary of a prescribed set of arbitrary control volumes (either the finite element partition itself or dual voronoi mesh, etc). The numerical approximations can be characterized as the solution of a constrained-minimization problem with constraints given by the flux conservation equations on each control volume. The discrete linear system is a typical saddle-point problem, but with less number of degrees of freedom than the Raviart-Thomas (for k>1) and the Brezzi-Douglas-Marini (for k>3) mixed finite element methods, where k denotes the degree of polynomial approximation spaces. Moreover, the numerical solution of the proposed scheme is of super-closeness with the finite element solution. Error estimates of optimal order are established for the numerical flux as well as the primary variable approximations. We present several numerical studies in order to verify convergence of the CFO schemes. Test cases under the presence of boundary layers, internal discontinuities, and a simplified two-phase flow in highly heterogeneous porous media model problem will also be presented. The numerical results show obvious advantages of applying high order CFO schemes.