Convergence analysis of some tent-based schemes for linear hyperbolic systems

Drake, Dow; Gopalakrishnan, Jay; Schöberl, Joachim; Wintersteiger, Christoph

doi:10.1090/mcom/3686

Convergence analysis of some tent-based schemes for linear hyperbolic systems
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by Dow Drake, Jay Gopalakrishnan, Joachim Schöberl and Christoph Wintersteiger;

Math. Comp. 91 (2022), 699-733

DOI: https://doi.org/10.1090/mcom/3686

Published electronically: September 22, 2021

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Abstract:

Finite element methods for symmetric linear hyperbolic systems using unstructured advancing fronts (satisfying a causality condition) are considered in this work. Convergence results and error bounds are obtained for mapped tent pitching schemes made with standard discontinuous Galerkin discretizations for spatial approximation on mapped tents. Techniques to study semidiscretization on mapped tents, design fully discrete schemes, prove local error bounds, prove stability on spacetime fronts, and bound error propagated through unstructured layers are developed.

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