An optimally stable approximation of reactive transport using discrete test and infinite trial spaces

Abstract

In this contribution we propose an optimally stable ultraweak Petrov-Galerkin variational formulation and subsequent discretization for stationary reactive transport problems. The discretization is exclusively based on the choice of discrete approximate test spaces, while the trial space is a priori infinite dimensional. The solution in the trial space or even only functional evaluations of the solution are obtained in a post-processing step. We detail the theoretical framework and demonstrate its usage in a numerical experiment that is motivated from modeling of catalytic filters.

revised version p.2: add comment and reference to the DPG and (FOS)LL* methods p.6 add footnote referencing the code repository p.7 add comment and reference on convergence rates under h-refinement