A posteriori error analysis for finite element solution of elliptic differential equations using equidistributing meshes

TL;DR

This paper develops an adaptive finite element method for elliptic differential equations using equidistributing meshes, based on residual-based a posteriori error estimates, and verifies convergence through theoretical analysis and numerical experiments.

Contribution

It introduces a new strategy for defining equidistributing meshes based on residual-based a posteriori error estimates and analyzes their convergence and dependence on the finite element solution.

Findings

Convergence of the finite element approximation is rigorously established.

Existence and computation methods for equidistributing meshes are provided.

Numerical results confirm the theoretical convergence and effectiveness.

Abstract

The paper is concerned with the adaptive finite element solution of linear elliptic differential equations using equidistributing meshes. A strategy is developed for defining this type of mesh based on residual-based a posteriori error estimates and rigorously analyzing the convergence of a linear finite element approximation using them. The existence and computation of equidistributing meshes and the continuous dependence of the finite element approximation on mesh are also studied. Numerical results are given to verify the theoretical findings.