Analysis of the SBP-SAT Stabilization for Finite Element Methods Part II: Entropy Stability

R. Abgrall, J. Nordström, P. Öffner, S. Tokareva

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

In the hyperbolic research community, there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability. In the first part of the series [6], the application of simultaneous approximation terms for linear problems is investigated where the boundary conditions are imposed weakly. By applying this technique, the authors demonstrate that a pure continuous Galerkin scheme is indeed linearly stable if the boundary conditions are imposed in the correct way. In this work, we extend this investigation to the nonlinear case and focus on entropy conservation. By switching to entropy variables, we provide an estimation of the boundary operators also for nonlinear problems, that guarantee conservation. In numerical simulations, we verify our theoretical analysis.

Original languageEnglish
Pages (from-to)573-595
Number of pages23
JournalCommunications on Applied Mathematics and Computation
Volume5
Issue number2
DOIs
Publication statusPublished - Jun 2023

Keywords

  • Continuous Galerkin
  • Entropy stability
  • Hyperbolic conservation laws
  • Initial-boundary value problem
  • Simultaneous approximation terms

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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