Superconvergence of Piecewise Linear Semi-Discretizations for Parabolic Equations with Nonuniform Triangulations

Abstract

In this paper we study the convergence properties of semi-discrete approximations for parabolic problems defined on two dimensional polygonal domains. These approximations are constructed using a nonstandard piecewise linear finite element method based on nonuniform triangulations of the domain and considering a variational formulation with a sesquilinear form which can be no strongly coercive. In order to increase accuracy a post-process procedure is studied.