High Order Maximum-Principle-Preserving Discontinuous Galerkin Method for Convection-Diffusion Equations

DOI10.1137/140965326zbMath1320.65145arXiv1404.4060OpenAlexW2055880686MaRDI QIDQ5254417

Tao Xiong, Jing-Mei Qiu, Zhengfu Xu

Publication date: 9 June 2015

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.4060

zbMATH Keywords

convection-diffusion equationshigh ordermaximum principle preservingflux limiterdiscoutinuous Galerkin method

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (max. 100)

Positivity-Preserving Local Discontinuous Galerkin Method for Pattern Formation Dynamical Model in Polymerizing Actin Flocks ⋮ Maximum-principle-preserving local discontinuous Galerkin methods for Allen-Cahn equations ⋮ High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments ⋮ High order conservative positivity-preserving discontinuous Galerkin method for stationary hyperbolic equations ⋮ A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Scalar Convection Diffusion Equations ⋮ Maximum principle preserving space and time flux limiting for diagonally implicit Runge-Kutta discretizations of scalar convection-diffusion equations ⋮ Bound-preserving discontinuous Galerkin methods with second-order implicit pressure explicit concentration time marching for compressible miscible displacements in porous media ⋮ A generalized Eulerian-Lagrangian discontinuous Galerkin method for transport problems ⋮ High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation ⋮ High-order bound-preserving discontinuous Galerkin methods for multicomponent chemically reacting flows ⋮ Maximum-principle-preserving high-order discontinuous Galerkin methods for incompressible Euler equations on overlapping meshes ⋮ Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes ⋮ Positivity preserving temporal second-order spatial fourth-order conservative characteristic methods for convection dominated diffusion equations ⋮ A simple bound-preserving sweeping technique for conservative numerical approximations ⋮ High order positivity-preserving nodal discontinuous Galerkin methods for anisotropic diffusion problems ⋮ Bound-Preserving Discontinuous Galerkin Method for Compressible Miscible Displacement in Porous Media ⋮ Quenching study of two-dimensional fractional reaction-diffusion equation from combustion process ⋮ Stability analysis and error estimates of local discontinuous Galerkin method for convection-diffusion equations on overlapping mesh with non-periodic boundary conditions ⋮ Positivity-preserving discontinuous Galerkin methods with Lax-Wendroff time discretizations ⋮ A fast method for solving time-dependent nonlinear convection diffusion problems ⋮ A positivity preserving characteristic finite element method for solving the transport and convection-diffusion-reaction equations on general surfaces ⋮ A positivity-preserving high order discontinuous Galerkin scheme for convection-diffusion equations ⋮ High-order bound-preserving discontinuous Galerkin methods for wormhole propagation on triangular meshes ⋮ Third order maximum-principle-satisfying DG schemes for convection-diffusion problems with anisotropic diffusivity ⋮ High-order bound-preserving finite difference methods for miscible displacements in porous media ⋮ High-order bound-preserving finite difference methods for incompressible wormhole propagation ⋮ Maximum-principle-preserving third-order local discontinuous Galerkin method for convection-diffusion equations on overlapping meshes ⋮ Stability analysis and error estimates of local discontinuous Galerkin methods for convection-diffusion equations on overlapping meshes ⋮ A high-order maximum-principle-satisfying discontinuous Galerkin method for the level set problem ⋮ Maximum principle and positivity-preserving high order spectral volume schemes with parametrized flux limiters for solving hyperbolic conservation laws ⋮ High-order bound-preserving discontinuous Galerkin methods for compressible miscible displacements in porous media on triangular meshes ⋮ Bound-preserving flux limiting for high-order explicit Runge-Kutta time discretizations of hyperbolic conservation laws

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A parametrized maximum principle preserving flux limiter for finite difference RK-WENO schemes with applications in incompressible flows
• High order parametrized maximum-principle-preserving and positivity-preserving WENO schemes on unstructured meshes
• A Petrov-Galerkin finite element method for convection-dominated flows: An accurate upwinding technique for satisfying the maximum principle
• On maximum-principle-satisfying high order schemes for scalar conservation laws
• Discrete maximum principle for parabolic problems solved by prismatic finite elements
• 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
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Discrete maximum principle for linear parabolic problems solved on hybrid meshes
• Efficient implementation of weighted ENO schemes
• New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
• Parametrized maximum principle preserving flux limiters for high order schemes solving multi-dimensional scalar hyperbolic conservation laws
• Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection-diffusion equations on triangular meshes
• Parametrized positivity preserving flux limiters for the high order finite difference WENO scheme solving compressible Euler equations
• Maximum-principle-satisfying High Order Finite Volume Weighted Essentially Nonoscillatory Schemes for Convection-diffusion Equations
• Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
• Parametrized maximum principle preserving flux limiters for high order schemes solving hyperbolic conservation laws: one-dimensional scalar problem
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Finite Volume Methods for Hyperbolic Problems
• Discrete maximum principles for nonlinear parabolic PDE systems
• High-Resolution Conservative Algorithms for Advection in Incompressible Flow
• Error Estimate on a Fully Discrete Local Discontinuous Galerkin Method for Linear Convection-Diffusion Problem
• Parametrized Maximum Principle Preserving Limiter for Finite Difference WENO Schemes Solving Convection-Dominated Diffusion Equations
• Discrete Maximum Principle and Adequate Discretizations of Linear Parabolic Problems
• A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives

This page was built for publication: High Order Maximum-Principle-Preserving Discontinuous Galerkin Method for Convection-Diffusion Equations