Stability analysis of explicit entropy viscosity methods for non-linear scalar conservation equations

DOI10.1090/S0025-5718-2013-02771-8zbMath1291.65277OpenAlexW2022930107MaRDI QIDQ5401691

Bojan Popov, Andrea Bonito, Jean-Luc Guermond

Publication date: 12 March 2014

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2013-02771-8

zbMATH Keywords

entropystabilityfinite element methodnumerical examplesBurgers equationlinear transport equationviscous approximationtime steppingnonlinear conservation equationexplicit Euler and Runge-Kutta methods

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) First-order hyperbolic equations (35L02)

Related Items (9)

Some Observations on the Interaction Between Linear and Nonlinear Stabilization for Continuous Finite Element Methods Applied to Hyperbolic Conservation Laws ⋮ A theoretical framework for discontinuity capturing: joining variational multiscale analysis and variation entropy theory ⋮ Analytical and variational numerical methods for unstable miscible displacement flows in porous media ⋮ Enriched Galerkin methods for two-phase flow in porous media with capillary pressure ⋮ Element centered smooth artificial viscosity in discontinuous Galerkin method for propagation of acoustic shock waves on unstructured meshes ⋮ Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization ⋮ A direct mixed-enriched Galerkin method on quadrilaterals for two-phase Darcy flow ⋮ Entropy stable method for the Euler equations revisited: central differencing via entropy splitting and SBP ⋮ Blending low-order stabilised finite element methods: a positivity-preserving local projection method for the convection-diffusion equation

Uses Software

• HLLE

Cites Work

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