On the Conservation and Convergence to Weak Solutions of Global Schemes

Authors:
Mark H. Carpenter;David Gottlieb;Chi-Wang Shu
Affiliations:
Computational Methods and Simulation Branch (CMSB), NASA Langley Research Center, Hampton, Virginia 23681-0001. m.h.carpenter@larc.nasa.gov;Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912. dig@cfm.brown.edu;Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912. shu@cfm.brown.edu
Venue:
Journal of Scientific Computing
Year:
2003

Citing 11
Cited 2

Analysis of the spectral vanishing viscosity method for periodic conservation laws

SIAM Journal on Numerical Analysis
Convergence of spectral methods for nonlinear conservation laws

SIAM Journal on Numerical Analysis
Legendre pseudospectral viscosity method for nonlinear conservation laws

SIAM Journal on Numerical Analysis
Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes

Journal of Computational Physics
Nonlinearly stable compact schemes for shock calculations

SIAM Journal on Numerical Analysis
The Chebyshev-Legendre method: implementing Legendre methods on Chebyshev points

SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Chebyshev--Legendre Spectral Viscosity Method for Nonlinear Conservation Laws

SIAM Journal on Numerical Analysis
Chebyshev--Legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws

SIAM Journal on Numerical Analysis
A stable and conservative interface treatment of arbitrary spatial accuracy

Journal of Computational Physics
On the Legendre–Gauss–Lobatto Points and Weights

Journal of Scientific Computing
Spectral Vanishing Viscosity Method For Nonlinear Conservation Laws

SIAM Journal on Numerical Analysis

Conservative hybrid compact-WENO schemes for shock-turbulence interaction

Journal of Computational Physics
Numerical Convergence Study of Nearly Incompressible, Inviscid Taylor-Green Vortex Flow

Journal of Scientific Computing

Quantified Score

Hi-index	0.01

Visualization

Abstract

In this paper we discuss the issue of conservation and convergence to weak solutions of several global schemes, including the commonly used compact schemes and spectral collocation schemes, for solving hyperbolic conservation laws. It is shown that such schemes, if convergent boundedly almost everywhere, will converge to weak solutions. The results are extensions of the classical Lax–Wendroff theorem concerning conservative schemes.