A high order conservative semi-Lagrangian discontinuous Galerkin method for two-dimensional transport simulations

DOI10.1007/s10915-017-0554-0zbMath1381.65081arXiv1612.06977OpenAlexW2962751174MaRDI QIDQ1691381

Xiaofeng Cai, Jing-Mei Qiu, Wei Guo

Publication date: 16 January 2018

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

Full work available at URL: https://arxiv.org/abs/1612.06977

zbMATH Keywords

numerical examplepositivity-preservinglinear transport equationsGreen's theoremnon-splittingconservative semi-Lagrangian discontinuous Galerkin methods

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Initial-boundary value problems for first-order hyperbolic equations (35L04)

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Cites Work

• A high order time splitting method based on integral deferred correction for semi-Lagrangian Vlasov simulations
• Arbitrarily high order convected scheme solution of the Vlasov-Poisson system
• Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: theoretical analysis and application to the Vlasov-Poisson system
• A discontinuous Galerkin method for the Vlasov-Poisson system
• Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system
• A high order characteristic discontinuous Galerkin scheme for advection on unstructured meshes
• A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equations
• High-performance high-resolution semi-Lagrangian tracer transport on a sphere
• A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid
• Selective monotonicity preservation in scalar advection
• On maximum-principle-satisfying high order schemes for scalar conservation laws
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• The Lagrange-Galerkin spectral element method on unstructured quadrilateral grids
• Efficient implementation of weighted ENO schemes
• A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows
• Characteristic Galerkin Methods for Scalar Conservation Laws in One Dimension
• The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• Stability of the Lagrange-Galerkin method with non-exact integration
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
• Eulerian‐Lagrangian localized adjoint method: The theoretical framework
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Conservative Semi-Lagrangian Finite Difference WENO Formulations with Applications to the Vlasov Equation
• High-Resolution Conservative Algorithms for Advection in Incompressible Flow
• The Mathematical Theory of Finite Element Methods
• Numerical Methods for Ordinary Differential Equations

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