A posteriorierror estimates forH¹-Galerkin mixed finite-element method for parabolic problems

Abstract

The purpose of this article is to derive a posteriori error estimates for the H 1 -Galerkin mixed finite element method for parabolic problems. We study both semidiscrete and fully discrete a posteriori error analyses using standard energy argument. A fully discrete a posteriori error analysis based on the backward Euler method is analysed and upper bounds for the errors are derived. The estimators yield upper bounds for the errors which are global in space and time. Our analysis is based on residual approach and the estimators are free from edge residuals.

Unconditional superconvergence analysis of an H1‐galerkin mixed finite element method for nonlinear Sobolev equations

“…To remove this restriction, an H 1 ‐Galerkin MFEM was proposed by Pani in , in which the approximation spaces can be chosen freely without the above restriction and the quasiuniformity of the meshes. Recently, such a method has been applied widely to many problems, such as integro‐differential equations and parabolic equations .…”