Convergence of second-order, entropy stable methods for multi-dimensional conservation laws

2019/06/12 by Chatterjee, Neelabja, Fjordholm, Ulrik Skre · 1 citation
#35L65 #65M08 (Secondary) #65M12 (Primary) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1906.05115

Abstract

High-order accurate, entropy stable numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space dimensions. In this paper we show how the entropy stability of one such method yields a (weak) bound on oscillations, and using compensated compactness we prove convergence to a weak solution satisfying at least one entropy condition.

Cited by

• A Neural Network for the Identical Kuramoto Equation: Architectural Considerations and Performance Evaluation

Related

• Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws
• Entropy Stable Space-Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws
• Entropy-stable discontinuous Galerkin difference methods for hyperbolic conservation laws
• Hyperbolic systems of conservation laws in one space dimension
• On the Convergence of Space-Time Discontinuous Galerkin Schemes for Scalar Conservation Laws