Post-processing and improved error estimates of numerical methods for evolutionary systems

Abstract We consider evolutionary systems, i.e., systems of linear partial differential equations arising from the mathematical physics. For these systems, there exists a general solution theory in exponentially weighted spaces, which can be exploited in the analysis of numerical methods. The numerical method considered in this paper is a discontinuous Galerkin method in time combined with a conforming Galerkin method in space. Building on our recent paper (Franz, S., Trostorff, S. & Waurick, M. (2019) Numerical methods for changing type systems. IMAJNA, 39, 1009–1038), we improve some of the results, study the dependence of the numerical solution on the weight parameter and consider a reformulation and post-processing of its numerical solution. As a by-product, we provide error estimates for the dG-C0 method. Numerical simulations support the theoretical findings.