Convergence analysis of some tent-based schemes for linear hyperbolic systems
Numerical Analysis
2021-07-15 v3 Numerical Analysis
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.
Cite
@article{arxiv.2101.04798,
title = {Convergence analysis of some tent-based schemes for linear hyperbolic systems},
author = {Dow Drake and Jay Gopalakrishnan and Joachim Schöberl and Christoph Wintersteiger},
journal= {arXiv preprint arXiv:2101.04798},
year = {2021}
}