This work was supported in part by NSF grant DMS-1912779
Mathematics of Computation
Hyperbolic functions, Wave equations, Boundary conditions, Asymptotic properties
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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Published as: Drake, 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.