Error estimate for a finite element approximation of the solution of a linear parabolic equation on a two-dimensional surface

TL;DR

This paper extends an error estimate for finite element approximations of the heat equation from flat domains to general linear parabolic equations on two-dimensional surfaces, broadening the applicability of the method.

Contribution

It generalizes existing error estimates for finite element methods from Euclidean domains to curved surfaces for linear parabolic equations.

Findings

Error estimate valid on surfaces

Extension from heat equation to general parabolic equations

Applicable to finite element approximations on 2D surfaces

Abstract

We show that a certain error estimate for a fully discrete finite element approximation of the solution of the heat equation which is defined in a two-dimensional Euclidean domain carries over to the case of a general linear parabolic equation which is defined on a two-dimensional surface.