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

Abstract

A nonconforming H 1 -Galerkin mixed finite element method is analyzed for Sobolev equations on anisotropic meshes. The error estimates are obtained without using Ritz-Volterra projection.

Extrapolated Expanded Mixed Finite Element Approximations of Semilinear Sobolev Equations

“…Due to these advantages, the mixed finite element method has been applied to some types of Sobolev equations by the authors in [8,10,11]. However the mixed finite element method is not useful to approximate the gradient from the flux because the flux term in (1.1)-(1.3) contains the mixed derivative with respect to the spatial and temporal variables.…”

A PRIORI L2ERROR ANALYSIS FOR AN EXPANDED MIXED FINITE ELEMENT METHOD FOR QUASILINEAR PSEUDO-PARABOLIC EQUATIONS

“…In [12], the authors constructed a numerical scheme to approximate the primal unknown u(x, t) and the unknown flux using a split least-squares characteristic MFEM for linear pseudo-parabolic equations with a convection term and d = 2. Shi and Wang [20] adopted a nonconforming Galerkin MFEM for linear pseudoparabolic equations with d = 2 on anisotropic meshes, and proved the error estimates in H 1 normed space. Shi and Zhang [21] introduced a new nonconforming finite element scheme based on a MFEM and an Euler fully discrete method for the linear pseudo-parabolic equation defined on Ω ⊂ R 2 and analyzed the optimal convergence of the error estimates.…”

Numerical Analysis of A Mixed Finite Element Method for Rosenau-Burgers Equation

“…Second, the polynomial degrees of the finite element spaces V h and W h may be different. Recently, many researchers have studied H 1 MFEM for second-order partial differential equations [7,8,9,10,11,12]. In 2012, Liu et al [12] first proposed and studied the H 1 MFEMs for fourth-order linear parabolic equation (…”