Dow, D., Gopalakrishnan, J., Schöberl, J., & Wintersteiger, C. (2022). Convergence analysis of some tent-based schemes for linear hyperbolic systems. Mathematics of Computation, 91(334), 699–733. https://doi.org/10.1090/mcom/3686
E101-03-1 - Forschungsgruppe Computational Mathematics in Engineering
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Journal:
Mathematics of Computation
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ISSN:
0025-5718
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Date (published):
2022
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Number of Pages:
35
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Publisher:
AMER MATHEMATICAL SOC
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Peer reviewed:
Yes
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Keywords:
Advancing front; Causality; Discontinuous galerkin; Friedrichs system; Mtp scheme; Sat timestepping; Semidiscrete; Spacetime; Stability; Taylor timestepping; Tent pitching
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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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Project (external):
NSF
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Project ID:
DMS-1912779
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Research Areas:
Computational Fluid Dynamics: 20% Mathematical and Algorithmic Foundations: 80%
