Functional a posteriori error estimate for a nonsymmetric stationary diffusion problem
It provides a rigorous error estimation framework for a class of diffusion problems, but the contribution is incremental as it extends existing functional-type estimates to nonsymmetric coefficients.
The paper derives guaranteed, method-independent a posteriori error estimates for nonsymmetric stationary diffusion problems and presents an algorithm for global minimization of the estimate using Raviart-Thomas elements, showing improvement with p-refinement.
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.