Characteristic Finite Element Method Research Articles

A wastewater treatment problem: study of the numerical convergence

We deal with the numerical approximation of a problem related to the management of sewage disposal and the design of wastewater treatment systems. We use a characteristics finite element method for the discretization of the state system. The main difficulty is due to the existence of Radon measures in the right-hand side of the system. We give convergence results and we present numerical experiences for a realistic problem.

Degenerate two-phase incompressible flow V: characteristic finite element methods

This is the fifth paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media. In this paper we study a finite element procedure for numerically solving this system. This procedure uses a mixed finite element method for the elliptic equation of the pressure and velocity and the modified method of characteristics for the degenerate parabolic equation of the saturation. Sharp error estimates in energy norms are obtained for this procedure. The error analysis does not use any regularization of the saturation equation and does not impose any restriction on the nature of degeneracy; these error estimates are derived directly from this degenerate saturation equation. Other characteristic finite element methods such as the modified method of characteristics with adjusted advection (MMOCAA) are also considered.

Improved error estimation of dynamic finite element methods for second-order parabolic equations

Dynamic finite element schemes are analyzed for second-order parabolic problems. These schemes permit different finite element spaces at different time levels in order to efficiently capture time-changing localized phenomena, such as moving sharp fronts or layers. The dynamical change of grids and interpolation polynomials is necessary and essential to many large-scale transient problems. Standard, characteristic, and mixed finite element methods with dynamic function spaces are considered for linear and nonlinear problems in a unified framework with improved a priori error estimates and convergence results.

Characteristic finite element methods for nonlinear Sobolev equations

In this paper, the time stepping along characteristic finite element methods for the nonlinear Sobolev equation is considered. Optimal convergence rates in H 1 and L 2 are demonstrated for this scheme. Numerical results published elsewhere have confirmed that larger time steps are appropriate with these scheme, and that the approximations exhibit improved qualitative behavior.

Characteristic finite element methods for diffusion epidemic models with age-structured populations

A numerical approximation is considered for a model of epidemiology describing age-dependent population dynamics with spatial diffusion. A finite difference method along the characteristic age-time direction is combined with finite elements in the spatial variable. Optimal order error estimates are derived for the approximation.

Characteristic finite element scheme and analysis the three-dimensional two-phase displacement semi-definite problem

NUMERICAL simulation of the two-phase (oil and water) displacement problem is the mathematical basis of energy sources. For two-dimensional positive problem, Douglas et al. put forward the well-known characteristic finite difference method and characteristic finite element method. However, for numerical analysis there exist some difficulties. They assumed that the problem is periodic and the diffusion matrix of the concentration equation is positive difinite in

The characteristic method applied to spin-coating in one dimension

In this paper spin coating of PMMA in chlorobenzene has been modelled using the characteristic finite element method. This method completely eliminates the numerical oscillations in the highly non-linear convection-diffusion equation solved under moving boundary conditions, which partially governs the mechanism of spin-coating. It is found that the mass transfer of the solvent by evaporation has a non-linear dependence on its initial concentration. The model is verified with experimental data for low as well as high molecular weight PMMA in chlorobenzene.

The characteristic streamline diffusion method for convection-diffusion problems

The paper describes an approximately characteristic finite element method for the solution of the time-dependent linear scalar convection-diffusion equation. The method is based on space-time elements approximately aligned with the characteristics in space-time. Attention is focused on implementation aspects: avoiding mesh tangling, efficient solution procedures and interpolation. Numerical results for some two-dimensional problems are given.

Finite element methods for one‐dimensional combustion problems

AbstractThree adaptive finite element methods based on equidistribution, elliptic grid generation and hybrid techniques are used to study a system of reaction–diffusion equations. It is shown that these techniques must employ sub‐equidistributing meshes in order to avoid ill‐conditioned matrices and ensure the convergence of the Newton method. It is also shown that elliptic grid generation methods require much longer computer times than hybrid and static rezoning procedures. The paper also includes characteristic, Petrov–Galerkin and flux‐corrected transport algorithms which are used to study a linear convection–reaction–diffusion equation that has an analytical solution. The flux‐corrected transport technique yields monotonic solutions in good agreement with the analytical solution, whereas the Petrov–Galerkin method with quadratic upstream‐weighted functions results in very diffused temperature profiles. The characteristic finite element method which uses a Lagrangian–Eulerian formulation overpredicts the flame front location and exhibits overshoots and undershoots near the temperature discontinuity. These overshoots and undershoots are due to the interpolation of the results of the Lagrangian operator onto the fixed Eulerian grid used to solve the reaction–diffusion operator, and indicate that characteristic finite element methods are not able to eliminate numerical diffusion entirely.

On a characteristic finite element method for compressible gas dynamics

In this paper, a generalization of the characteristic finite clement method for compressible. viscous gas dynamics is presented. Some preliminary numerical results illustrate the concept of the method.

特性曲線型有限要素法を用いた密度差のある地下水流動の数値解析-淡水・塩水2相流への応用

特性曲線型有限要素法を用いた密度差のある地下水流動の数値解析-淡水・塩水2相流への応用