Conforming and Non-Conforming Functional A Posteriori Error Estimates for Elliptic Boundary Value Problems in Exterior Domains: Theory and Numerical Tests

TL;DR

This paper develops conforming and non-conforming functional a posteriori error estimates for elliptic boundary value problems in exterior domains, providing guaranteed bounds and extending previous results to non-conforming approximations, supported by numerical tests.

Contribution

It extends existing a posteriori error estimates to non-conforming solutions in exterior elliptic problems, including theoretical derivations and numerical validation.

Findings

Guaranteed upper and lower bounds for errors

Extension of estimates to non-conforming approximations

Numerical tests confirming theoretical results

Abstract

This paper is concerned with the derivation of conforming and non-conforming functional a posteriori error estimates for elliptic boundary value problems in exterior domains. These estimates provide computable and guaranteed upper and lower bounds for the difference between the exact and the approximate solution of the respective problem. We extend earlier results for conforming approximations to the non-conforming case, for which the approximate solutions might not belong to the energy space and are just considered to be square integrable. Moreover, we present some numerical tests.