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

on the occasion of his 60th birthday This paper is concerned with the derivation of conforming and non-conforming functional a posteriori error estimates for elliptic boundary value problems in exte-rior 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 the results from [5] to non-conforming approxima-tions, which might not belong to the energy space and are just considered to be square integrable. Moreover, we present some numerical tests. Key Words functional a posteriori error estimates, elliptic boundary value prob-lems, exterior domains, non-conforming approximation