Stability conditions for the numerical solution of convection-dominated\n problems with skew-symmetric discretizations

2010/07/19 by Erwan Deriaz, Deriaz, Erwan
Computer Science · Engineering · Mathematics · #65M05 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1007.3313

openalex publication_date 2010/07/19 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

This paper presents original and close to optimal stability conditions\nlinking the time step and the space step, stronger than the CFL criterion:\n\δ t\≤ C\δ x^\α with \α=\(2r)/(2r-1), r an integer,\nfor some numerical schemes we produce, when solving convection-dominated\nproblems. We test this condition numerically and prove that it applies to\nnonlinear equations under smoothness assumptions.\n

Citations

• Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
• Strong Stability-Preserving High-Order Time Discretization Methods

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