Optimal strong-stability-preserving Runge-Kutta time discretizations for discontinuous Galerkin methods

DOI10.1007/s10915-013-9796-7zbMath1304.65219OpenAlexW2087667894MaRDI QIDQ474942

Ethan J. Kubatko, Benjamin A. Yeager, David I. Ketcheson

Publication date: 25 November 2014

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

Full work available at URL: https://doi.org/10.1007/s10915-013-9796-7

zbMATH Keywords

semidiscretizationhyperbolic conservation lawsstrong-stability-preservingCourant-Friedrichs-Lewy stability constraintsdiscontinuous Galerkin spatial discretizationsnumerical test casesRunge-Kutta time steppers

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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (35)

An arbitrary high-order spectral difference method for the induction equation ⋮ High-order multirate explicit time-stepping schemes for the baroclinic-barotropic split dynamics in primitive equations ⋮ Efficient computation of time-periodic compressible flows with spectral techniques ⋮ Strong stability preserving explicit peer methods for discontinuous Galerkin discretizations ⋮ Second Order Implicit Schemes for Scalar Conservation Laws ⋮ Optimized explicit Runge-Kutta schemes for high-order collocated discontinuous Galerkin methods for compressible fluid dynamics ⋮ Strong stability preserving transformed DIMSIMs ⋮ Strong Stability Preserving Integrating Factor Runge--Kutta Methods ⋮ Multiple time scales and pressure forcing in discontinuous Galerkin approximations to layered ocean models ⋮ Third-order paired explicit Runge-Kutta schemes for stiff systems of equations ⋮ Arbitrary high-order explicit hybridizable discontinuous Galerkin methods for the acoustic wave equation ⋮ Comparison of implicit and explicit hybridizable discontinuous Galerkin methods for the acoustic wave equation ⋮ Fully-discrete analysis of high-order spatial discretizations with optimal explicit Runge-Kutta methods ⋮ A Well-Balanced Scheme for Euler Equations with Singular Sources ⋮ Optimal explicit Runge-Kutta time stepping for density-based finite-volume solvers ⋮ Implicit and implicit-explicit strong stability preserving Runge-Kutta methods with high linear order ⋮ Melting interfaces in induction heated bodies ⋮ Embedded paired explicit Runge-Kutta schemes ⋮ Strong stability preserving second derivative general linear methods based on Taylor series conditions for discontinuous Galerkin discretizations ⋮ A discontinuous Galerkin finite element model for compound flood simulations ⋮ Many-stage optimal stabilized Runge-Kutta methods for hyperbolic partial differential equations ⋮ Conservative explicit local time-stepping schemes for the shallow water equations ⋮ Optimal Runge-Kutta schemes for pseudo time-stepping with high-order unstructured methods ⋮ Paired explicit Runge-Kutta schemes for stiff systems of equations ⋮ A robust CFL condition for the discontinuous Galerkin method on triangular meshes ⋮ The discontinuous Galerkin method: derivation and properties ⋮ Time step restrictions for strong-stability-preserving multistep Runge-Kutta discontinuous Galerkin methods ⋮ Optimal Runge-Kutta stability polynomials for multidimensional high-order methods ⋮ Stability of nonlinear convection-diffusion-reaction systems in discontinuous Galerkin methods ⋮ Design of IMEXRK time integration schemes via Delaunay-based derivative-free optimization with nonconvex constraints and grid-based acceleration ⋮ High order explicit local time stepping methods for hyperbolic conservation laws ⋮ Numerical considerations for quantifying air-water turbulence with moment field equations ⋮ An admissibility and asymptotic preserving scheme for systems of conservation laws with source term on 2D unstructured meshes with high-order MOOD reconstruction ⋮ Numerical approximation of generalized Burger's-Fisher and generalized Burger's-Huxley equation by compact finite difference method ⋮ High-order flux reconstruction schemes with minimal dispersion and dissipation

Uses Software

• CVX

Cites Work

• Unnamed Item
• Optimal Runge-Kutta schemes for discontinuous Galerkin space discretizations applied to wave propagation problems
• Implementation of a discontinuous Galerkin morphological model on two-dimensional unstructured meshes
• Dynamic \(p\)-adaptive Runge-Kutta discontinuous Galerkin methods for the shallow water equations
• Local time-stepping in Runge-Kutta discontinuous Galerkin finite element methods applied to the shallow-water equations
• One step integration methods with maximum stability regions
• Stability of the method of lines
• Semi discrete discontinuous Galerkin methods and stage-exceeding-order, strong-stability-preserving Runge-Kutta time discretizations
• High resolution schemes for hyperbolic conservation laws
• New stability theorems concerning one-step numerical methods for ordinary differential equations
• Low-storage Runge-Kutta schemes
• Strong stability preserving properties of Runge--Kutta time discretization methods for linear constant coefficient operators
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods
• Optimal stability polynomials for numerical integration of initial value problems
• Positivity-preserving DG and central DG methods for ideal MHD equations
• A parallel local timestepping Runge-Kutta discontinuous Galerkin method with applications to coastal Ocean modeling
• Multirate timestepping methods for hyperbolic conservation laws
• High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms
• Explicit Runge-Kutta formulas with increased stability boundaries
• Strong Stability-Preserving High-Order Time Discretization Methods
• Graph Implementations for Nonsmooth Convex Programs
• The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Largest disk of stability of explicit Runge-Kutta methods
• Total variation diminishing Runge-Kutta schemes
• A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
• Optimized Explicit Runge--Kutta Schemes for the Spectral Difference Method Applied to Wave Propagation Problems
• Highly Efficient Strong Stability-Preserving Runge–Kutta Methods with Low-Storage Implementations
• Representations of Runge--Kutta Methods and Strong Stability Preserving Methods
• Global optimization of explicit strong-stability-preserving Runge-Kutta methods
• Numerical Methods for Ordinary Differential Equations

This page was built for publication: Optimal strong-stability-preserving Runge-Kutta time discretizations for discontinuous Galerkin methods