A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach

DOI10.1090/S0025-5718-96-00701-6zbMath0848.65067MaRDI QIDQ4878567

Bernardo Cockburn, Pierre Alain Gremaud

Publication date: 27 October 1996

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

error estimatesconservation lawsEngquist-Osher schemeKuznetsov approximation

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (17)

Error estimates for forward Euler shock capturing finite element approximations of the one-dimensional Burgers' equation ⋮ Error Estimates of a First-order Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations ⋮ 𝐿¹ error estimates for difference approximations of degenerate convection-diffusion equations ⋮ Analysis of space-time discontinuous Galerkin method for nonlinear convection-diffusion problems ⋮ Finite volume relaxation schemes for multidimensional conservation laws ⋮ An optimal error estimate for upwind finite volume methods for nonlinear hyperbolic conservation laws ⋮ Computation of compressible flows with high density ratio and pressure ratio ⋮ A priori error estimates for upwind finite volume schemes for two-dimensional linear convection diffusion problems ⋮ 𝐿¹–framework for continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations ⋮ Error estimates for higher-order finite volume schemes for convection-diffusion problems ⋮ Second-Order Convergence of Monotone Schemes for Conservation Laws ⋮ Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients ⋮ A posteriorierror estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations ⋮ A review of a posteriori error control and adaptivity for approximations of non‐linear conservation laws ⋮ Error estimate for the upwind finite volume method for the nonlinear scalar conservation law ⋮ A priori error estimates for numerical methods for scalar conservation laws. Part II : flux-splitting monotone schemes on irregular Cartesian grids ⋮ Convergence and error estimates of relaxation schemes for multidimensional conservation laws

Cites Work

• Measure-valued solutions to conservation laws
• A posteriori error estimates for general numerical methods for scalar conservation laws
• On Convergence of Monotone Finite Difference Schemes with Variable Spatial Differencing
• Quasimonotone Schemes for Scalar Conservation Laws Part I
• Quasimonotone Schemes for Scalar Conservation Laws. Part II
• Error Bounds for the Methods of Glimm, Godunov and LeVeque
• A Moving Mesh Numerical Method for Hyperbolic Conservation Laws
• Riemann Solvers, the Entropy Condition, and Difference
• On Nonlocal Monotone Difference Schemes for Scalar Conservation Laws
• The Neumann Problem for Nonlinear Second Order Singular Perturbation Problems
• One-Sided Difference Approximations for Nonlinear Conservation Laws
• The Significance of the Stability of Difference Schemes in Different $l^p $-Spaces
• Convergence of Finite Difference Schemes for Conservation Laws in Several Space Dimensions: The Corrected Antidiffusive Flux Approach
• Convergence of a streamline diffusion finite element method for scalar conservation laws with boundary conditions
• On finite-difference approximations and entropy conditions for shocks
• On the piecewise smoothness of entropy solutions to scalar conservation laws
• Convergence of Upwind Finite Volume Schemes for Scalar Conservation Laws in Two Dimensions
• An Error Estimate for Finite Volume Methods for Multidimensional Conservation Laws
• Convergence of a Shock-Capturing Streamline Diffusion Finite Element Method for a Scalar Conservation Law in Two Space Dimensions
• Convergence of the Finite Volume Method for Multidimensional Conservation Laws
• A Stable Adaptive Numerical Scheme for Hyperbolic Conservation Laws
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