Convergence and error estimates in finite volume schemes for general multidimensional scalar conservation laws. I. Explicite monotone schemes

DOI10.1051/m2an/1994280302671zbMath0823.65087OpenAlexW2286355715MaRDI QIDQ4698881

Jean-Paul Vila

Publication date: 24 October 1995

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/193739

zbMATH Keywords

convergencefinite volume schemeserror estimatescalar conservation lawsmultidimensionalmonotone scheme

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (19)

An error bound for the polygonal approximation of conservation laws with source terms ⋮ Error estimates of the Godunov method for the multidimensional compressible Euler system ⋮ Finite volume schemes for elliptic and elliptic-hyperbolic problems on triangular meshes ⋮ Error estimate for finite volume scheme ⋮ Error estimates for scalar conservation laws by a kinetic approach ⋮ Development of a refinement criterion for adaptive mesh refinement in steam-assisted gravity drainage simulation ⋮ Finite volume relaxation schemes for multidimensional conservation laws ⋮ Convergence of implicit Finite Volume methods for scalar conservation laws with discontinuous flux function ⋮ A priori error estimates for upwind finite volume schemes for two-dimensional linear convection diffusion problems ⋮ Error estimates for higher-order finite volume schemes for convection-diffusion problems ⋮ Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes ⋮ Splitting method applied to hyperbolic problem with source term ⋮ 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 ⋮ Probabilistic analysis of the upwind scheme for transport equations ⋮ Parallel discontinuous Galerkin unstructured mesh solvers for the calculation of three-dimen\-sion\-al wave propagation problems ⋮ L²-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes ⋮ Error Estimate for Time-Explicit Finite Volume Approximation of Strong Solutions to Systems of Conservation Laws ⋮ A priori error estimates for numerical methods for scalar conservation laws. Part II : flux-splitting monotone schemes on irregular Cartesian grids

Cites Work

• Convergence of an upstream finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh
• Measure-valued solutions to conservation laws
• Numerical Viscosity and the Entropy Condition for Conservative Difference Schemes
• Riemann Solvers, the Entropy Condition, and Difference
• Monotone Difference Approximations for Scalar Conservation Laws
• Some Relations Between Nonexpansive and Order Preserving Mappings
• Convergence of Finite Difference Schemes for Conservation Laws in Several Space Dimensions: The Corrected Antidiffusive Flux Approach
• On the Continuity in BV (Ω) of the L 2 -Projection into Finite Element Spaces
• Convergence of a streamline diffusion finite element method for scalar conservation laws with boundary conditions
• Convergence d'un schéma décentré amont sur un maillage triangulaire pour un problème hyperbolique linéaire
• Accuracy of some approximate methods for computing the weak solutions of a first-order quasi-linear equation
• Numerical Viscosity and Convergence of Finite Volume Methods for Conservation Laws with Boundary Conditions
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Convergence and error estimates in finite volume schemes for general multidimensional scalar conservation laws. I. Explicite monotone schemes