Analysis of the implicit upwind finite volume scheme with rough coefficients

DOI10.1007/s00211-017-0935-1zbMath1395.65041arXiv1702.02534OpenAlexW3101457736MaRDI QIDQ1749440

André Schlichting, Christian Seis

Publication date: 16 May 2018

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.02534

zbMATH Keywords

weak convergencerough initial dataKantorovich-Rubinstein distanceimplicit upwind finite volume schemeunstructured regular mesh

Mathematics Subject Classification ID

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) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

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Cites Work

• Existence and uniqueness of maximal regular flows for non-smooth vector fields
• Transport equation and Cauchy problem for BV vector fields
• Probabilistic analysis of the upwind scheme for transport equations
• Error estimate for finite volume scheme
• Ordinary differential equations, transport theory and Sobolev spaces
• Convergence of an explicit finite volume scheme for first order symmetric systems
• A quantitative theory for the continuity equation
• Convergence order of upwind type schemes for transport equations with discontinuous coefficients
• Crossover of the coarsening rates in demixing of binary viscous liquids
• Upper Bounds on Coarsening Rates in Demixing Binary Viscous Liquids
• A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• Estimates and regularity results for the DiPerna-Lions flow
• $L^\infty$- and $L^2$-Error Estimates for a Finite Volume Approximation of Linear Advection
• Analysis of the upwind finite volume method for general initial- and boundary-value transport problems
• Convergence of the Discontinuous Galerkin Method for Discontinuous Solutions
• An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• The Sharpness of Kuznetsov's O(√Δx)L 1 -Error Estimate for Monotone Difference Schemes
• Convergence Rates for Upwind Schemes with Rough Coefficients
• Optimal Order of Convergence for the Upwind Scheme for the Linear Advection on a Bounded Domain
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