L$^2$ Error Estimate to Smooth Solutions of High Order Runge--Kutta Discontinuous Galerkin Method for Scalar Nonlinear Conservation Laws with and without Sonic Points
From MaRDI portal
Publication:5093636
DOI10.1137/21M1435495zbMath1501.65062MaRDI QIDQ5093636
No author found.
Publication date: 29 July 2022
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
error estimatenonlinear conservation lawnumerical fluxRunge-Kutta discontinuous Galerkin methodsonic point
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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)
Related Items
Spatio‐temporal scalar auxiliary variable approach for the nonlinear convection–diffusion equation with discontinuous Galerkin method, Superconvergence of projection integrators for conservative system
Cites Work
- Unnamed Item
- Unnamed Item
- Dynamic \(p\)-adaptive Runge-Kutta discontinuous Galerkin methods for the shallow water equations
- Superconvergence analysis of the Runge-Kutta discontinuous Galerkin methods for a linear hyperbolic equation
- Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations
- 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
- Dynamic models for large eddy simulation of compressible flows with a high order DG method
- A locally \(p\)-adaptive approach for large eddy simulation of compressible flows in a DG framework
- Analysis of discontinuous Galerkin methods with upwind-biased fluxes for one dimensional linear hyperbolic equations with degenerate variable coefficients
- Local error estimates for Runge-Kutta discontinuous Galerkin methods with upwind-biased numerical fluxes for a linear hyperbolic equation in one-dimension with discontinuous initial data
- A numerical study for the performance of the Runge-Kutta discontinuous Galerkin method based on different numerical fluxes
- Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations
- Application of generalized Gauss–Radau projections for the local discontinuous Galerkin method for linear convection-diffusion equations
- Superconvergence of Discontinuous Galerkin methods based on upwind-biased fluxes for 1D linear hyperbolic equations
- Explicit Runge–Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems
- 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
- Riemann Solvers and Numerical Methods for Fluid Dynamics
- TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
- On a Cell Entropy Inequality for Discontinuous Galerkin Methods
- Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
- An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
- Superconvergence of Discontinuous Galerkin Methods for Scalar Nonlinear Conservation Laws in One Space Dimension
- Error Estimate of the Fourth-Order Runge--Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations
- Discontinuous Galerkin Methods for Nonlinear Scalar Conservation Laws: Generalized Local Lax--Friedrichs Numerical Fluxes
- The L$^2$-norm Stability Analysis of Runge--Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations
- Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge–Kutta Discontinuous Galerkin Method for Scalar Conservation Laws
- Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments
- The Mathematical Theory of Finite Element Methods
- A priorierror estimates to smooth solutions of the third order Runge–Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws
- Error Estimates to Smooth Solutions of Runge–Kutta Discontinuous Galerkin Method for Symmetrizable Systems of Conservation Laws
