Functional a posteriori error estimate for a nonsymmetric stationary diffusion problem

TL;DR

This paper develops guaranteed functional a posteriori error estimates for nonsymmetric stationary diffusion problems, providing a method to minimize the error estimate over flux spaces, with numerical validation using Raviart-Thomas elements.

Contribution

It introduces a guaranteed a posteriori error estimate for nonsymmetric diffusion problems and an algorithm for its global minimization over flux spaces, independent of numerical methods.

Findings

Error bounds improve with p-refinement of Raviart-Thomas spaces

Global minimization effectively reduces the error estimate

Numerical tests confirm the theoretical error reduction

Abstract

In this paper, a posteriori error estimates of functional type for a stationary diffusion problem with nonsymmetric coefficients are derived. The estimate is guaranteed and does not depend on any particular numerical method. An algorithm for the global minimization of the error estimate with respect to the flux over some finite dimensional subspace is presented. In numerical tests, global minimization is done over the subspace generated by Raviart-Thomas elements. The improvement of the error bound due to the p-refinement of these spaces is investigated.