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

Renelt, Lukas; Ohlberger, Mario; Engwer, Christian

Research article in edited proceedings (conference) | Peer reviewed

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.

Details about the publication

Editors: Franck, Emmanuel; Fuhrmann, Jürgen;, Michel-Dansac, Victor; Navoret, Laurent

Book title: Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems (Volume 2)

Page range: 289-298

Publisher: Springer

Place of publication: Cham

Title of series: Springer Proceedings in Mathematics & Statistics (ISSN: 2194-1017)

Status: Published

Release year: 2023 (13/10/2023)

Language in which the publication is written: English

Conference: International Conference on Finite Volumes for Complex Applications, Strasbourg, France

ISBN: 978-3-031-40860-1

DOI: 10.1007/978-3-031-40860-1_30

Link to the full text: https://link.springer.com/chapter/10.1007/978-3-031-40860-1_30

Keywords: optimal stability; reactive transport; ultraweak formulation

Authors from the University of Münster

Engwer, Christian	Professorship for Applications of Partial Differential Equations Center for Data Science and Complexity (CDSC)
Ohlberger, Mario	Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger) Center for Data Science and Complexity (CDSC) Center for Multiscale Theory and Computation (CMTC)
Renelt, Lukas	Professorship for Applications of Partial Differential Equations Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)

Projects the publication originates from

ML-MORE: Machine learning and model order reduction to predict the efficiency of catalytic filters. Subproject 1: Model Order Reduction (ML-MORE) Duration: 01/04/2020 - 31/12/2023 Funded by: Federal Ministry of Research, Technology and Space Type of project: Participation in federally funded joint project
Cluster of Excellence 2044 - Mathematics Münster: Dynamics – Geometry – Structure (EXC 2044) Duration: 01/01/2019 - 31/12/2025 \| 1st Funding period Funded by: DFG - Cluster of Excellence Type of project: Main DFG-project hosted at University of Münster

Talks on the publication

An optimally stable numerical scheme for reactive transport
Renelt, Lukas (31/10/2023)
Posterpresentation at Finite Volumes for Complex Applications 10 (FVCA10), Strasbourg
Type of talk: scientific Talk

Doctorates the publication originates from

Numerical methods for Friedrichs’ systems: Approximation theory, localized training and inherently stable model order reduction
Candidate: Renelt, Lukas | Supervisors: Ohlberger, Mario; Engwer, Christian | Reviewers: Ohlberger, Mario; Engwer, Christian; Vohralík; Martin
Period of time: 01/02/2021 - 10/01/2025
Doctoral examination procedure finished at: Doctoral examination procedure at University of Münster