A conservative Eulerian-Lagrangian Runge-Kutta discontinuous Galerkin method for linear hyperbolic system with large time stepping

DOI10.1007/s10915-024-02452-1arXiv2207.13736MaRDI QIDQ6123344

Xue Hong, Jing-Mei Qiu

Publication date: 4 March 2024

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.13736

zbMATH Keywords

characteristic methoddiscontinuous GalerkinEulerian-Lagrangianlinear hyperbolic systemconservative property

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element methods applied to problems in fluid mechanics (76M10) Magnetohydrodynamics and electrohydrodynamics (76W05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) First-order hyperbolic equations (35L02)

Cites Work

• Unnamed Item
• Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: theoretical analysis and application to the Vlasov-Poisson system
• A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equations
• A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media
• A semi-Lagrangian discontinuous Galerkin (DG)-local DG method for solving convection-diffusion equations
• A high order conservative semi-Lagrangian discontinuous Galerkin method for two-dimensional transport simulations
• An Eulerian-Lagrangian discontinuous Galerkin method for transport problems and its application to nonlinear dynamics
• Discontinuous Galerkin semi-Lagrangian method for Vlasov-Poisson
• Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: Analysis and application in one dimension
• The numerical solution of hyperbolic systems of partial differential equations in three independent variables
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Explicit Finite Element Methods for Symmetric Hyperbolic Equations
• Evolution Galerkin methods for hyperbolic systems in two space dimensions
• Enhanced accuracy by post-processing for finite element methods for hyperbolic equations
• A Conservative Semi-Lagrangian Hybrid Hermite WENO Scheme for Linear Transport Equations and the Nonlinear Vlasov--Poisson System
• Arbitrary Lagrangian--Eulerian Discontinuous Galerkin Method for Hyperbolic Equations Involving $\delta$-Singularities
• An Eulerian‐Lagrangian discontinuous Galerkin method for transient advection‐diffusion equations
• A high‐order triangular discontinuous Galerkin oceanic shallow water model
• Convergence Analysis of a Discontinuous Galerkin/Strang Splitting Approximation for the Vlasov--Poisson Equations

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