Stability analysis and error estimates of arbitrary Lagrangian–Eulerian discontinuous Galerkin method coupled with Runge–Kutta time-marching for linear conservation laws

DOI10.1051/m2an/2018069zbMath1418.65141OpenAlexW2927818051MaRDI QIDQ5226423

Lingling Zhou, Chi-Wang Shu, Yinhua Xia

Publication date: 31 July 2019

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/m2an/2018069

zbMATH Keywords

stabilityerror estimatesconservation lawsRunge-Kutta methodsarbitrary Lagrangian-Eulerian discontinuous Galerkin method

Mathematics Subject Classification ID

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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An Eulerian-Lagrangian discontinuous Galerkin method for transport problems and its application to nonlinear dynamics ⋮ Arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for KdV type equations ⋮ A generalized Eulerian-Lagrangian discontinuous Galerkin method for transport problems ⋮ A Method-of-Lines Framework for Energy Stable Arbitrary Lagrangian–Eulerian Methods ⋮ New finite volume element methods in the ALE framework for time-dependent convection-diffusion problems in moving domains ⋮ Arbitrary Lagrangian--Eulerian Discontinuous Galerkin Method for Hyperbolic Equations Involving $\delta$-Singularities ⋮ Arbitrary Lagrangian-Eulerian local discontinuous Galerkin method for linear convection-diffusion equations ⋮ Strong Stability of Explicit Runge--Kutta Time Discretizations ⋮ Superconvergence of Arbitrary Lagrangian--Eulerian Discontinuous Galerkin Methods for Linear Hyperbolic Equations ⋮ The positivity preserving property on the high order arbitrary Lagrangian-Eulerian discontinuous Galerkin method for Euler equations

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