Explicit Consistency Error Estimate for Finite Element Solutions of the Poisson Equation on Convex Domains

TL;DR

This paper derives explicit a priori consistency error estimates for finite element solutions of the Poisson equation on convex domains, with estimates depending only on geometric parameters and applicable to various meshes.

Contribution

It provides the first explicit consistency error bounds for finite element discretizations on convex domains with domain approximation by convex polyhedra.

Findings

Explicit error estimates depend only on geometric parameters.

Applicable to general convex domains and arbitrary simplicial meshes.

Enhances understanding of finite element accuracy on convex geometries.

Abstract

We derive explicit a priori consistency error estimates for a standard finite element discretization of the Poisson equation on convex domains, where the domain is approximated by an internal convex polyhedron. The obtained explicit estimates depend only on global geometric parameters and are applicable to general convex domains and arbitrary families of simplicial meshes.