Post-processing and improved error estimates of numerical methods for evolutionary systems
Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung
Beitragende
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.
Details
Originalsprache | Englisch |
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Seitenumfang | 23 |
Fachzeitschrift | IMA journal of numerical analysis |
Publikationsstatus | Elektronische Veröffentlichung vor Drucklegung - Okt. 2023 |
Peer-Review-Status | Ja |
Externe IDs
ORCID | /0000-0002-2458-1597/work/149797109 |
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Schlagworte
Schlagwörter
- dG-C0 method, discontinuous Galerkin, Evolutionary equations, Post-processing, Space-time approach