H1-Galerkin Mixed Finite Element Research Articles

A new mixed scheme based on variation of constants for Sobolev equation with nonlinear convection term

A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear convection term. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are given to confirm the theoretical analysis of the proposed method.

An Error Estimates for Convection Dominated Diffusion Problems

In classical mixed finite element method, the choice of the finite element approximating spaces is restricted by the imposition of the LBB consistency condition. The method of H1- Galerkin mixed finite element method avoids completely the imposition of such a condition on the approximating spaces. In this article, we discuss and analyze error estimates for Convection- dominated diffusion problems using H1-Galerkin mixed finite element method, along with the method of characteristics. Optimal order of convergence has been achieved for the error estimates of a single-step Euler backward difference scheme. Keywords. H1- Galerkin mixed finite element method, Characteristics method, LBB condition, optimal error estimates, and Euler backward difference scheme.

Optimal Convergence Analysis for Convection Dominated Diffusion Problems

In classical mixed finite element method, the choice of the finite element approximating spaces is restricted by the imposition of the LBB consistency condition. The method of H1-Galerkin mixed finite element method avoids completely the imposition of such a condition on the approximating spaces. In this article, we discuss and analyze error estimates for Convection-dominated diffusion problems using H1-Galerkin mixed finite element method, along with the method of characteristics. Optimal order of convergence has been achieved for the error estimates of a two-step Euler backward difference scheme.

Nonconforming <i>H</i><sup>1</sup>-Galerkin Mixed Finite Element Method for Pseudo-Hyperbolic Equations

Based on H1-Galerkin mixed finite element method with nonconforming quasi-Wilson element, a numerical approximate scheme is established for pseudo-hyperbolic equations under arbitrary quadrilateral meshes. The corresponding optimal order error estimate is derived by the interpolation technique instead of the generalized elliptic projection which is necessary for classical error estimates of finite element analysis.

H<sup>1</sup> -Galerkin Expanded Mixed Finite Element Methods for Pseudo-Hyperbolicequations

H1-Galerkin mixed finite element method combining with expanded mixed element method are discussed for a class of second-order pseudo-hyperbolic equations. The methods possesses the advantage of mixed finite element while avoiding directly inverting the permeability tensor, which is important especially in a low permeability zone. Depended on the physical quantities of interest, the methods are discussed. The existence and uniqueness of numerical solutions of the scheme are derived and an optimal order error estimate for the methods is obtained.

An optimal‐order error estimate on an H1‐Galerkin mixed method for a nonlinear parabolic equation in porous medium flow

AbstractWe present an H1‐Galerkin mixed finite element method for a nonlinear parabolic equation, which models a compressible fluid flow process in subsurface porous media. The method possesses the advantages of mixed finite element methods while avoiding directly inverting the permeability tensor, which is important especially in a low permeability zone. We conducted theoretical analysis to study the existence and uniqueness of the numerical solutions of the scheme and prove an optimal‐order error estimate for the method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

Nonconforming H 1-Galerkin mixed FEM for Sobolev equations on anisotropic meshes

A nonconforming H1-Galerkin mixed finite element method is analyzed for Sobolev equations on anisotropic meshes. The error estimates are obtained without using Ritz-Volterra projection.

H1-Galerkin Mixed Finite Element Method for the Regularized Long Wave Equation

In this paper, an H1-Galerkin mixed finite element method is proposed for the 1-D regularized long wave (RLW) equation ut + ux + uux - δuxxt = 0. The existence of unique solutions of the semi-discrete and fully discrete H1-Galerkin mixed finite element methods is proved, and optimal error estimates are established. Our method can simultaneously approximate the scalar unknown and the vector flux effectively, without requiring the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

H1-Galerkin mixed finite element methods for parabolic partial integro-differential equations

H1‐Galerkin mixed finite element methods are analysed for parabolic partial integro‐differential equations which arise in mathematical models of reactive flows in porous media and of materials with memory effects. Depending on the physical quantities of interest, two methods are discussed. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. An extension to problems in two and three space variables is also discussed and it is shown that the H1‐Galerkin mixed finite element approximations have the same rate of convergence as in the classical methods without requiring the LBB consistency condition.

AnH1-Galerkin Mixed Finite Element Method for an Evolution Equation with a Positive-Type Memory Term

An H1-Galerkin mixed finite element method is analyzed for a class of evolution equations with memory. When a classical mixed method is applied to such problems, it has not been possible to obtain any estimate for the flux. However, the proposed approach yields optimal order convergence without the LBB consistency condition and quasi uniformity of the finite element mesh. Compared to the results proved for one space variable, the L2 estimate of the flux is not optimal for problems in two and three space dimensions. Therefore, a modification of the method is proposed and analyzed. A maximum norm estimate is also derived in one and two space variables. A backward Euler approximation of the modified method is also analyzed.