Convergence Analysis of the Upwind Finite Volume Scheme for General Transport Problems

DOI10.1007/978-3-642-20671-9_17zbMath1246.76068OpenAlexW2208475935MaRDI QIDQ2902082

Franck Boyer

Publication date: 17 August 2012

Published in: Finite Volumes for Complex Applications VI Problems & Perspectives (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-20671-9_17

zbMATH Keywords

transport equationrenormalized solutionsupwind finite volume method

Mathematics Subject Classification ID

Finite volume methods applied to problems in fluid mechanics (76M12) Weak solutions to PDEs (35D30) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Initial-boundary value problems for first-order hyperbolic equations (35L04)

Cites Work

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• 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
• Trace theorems and spatial continuity properties for the solutions of the transport equation.
• An Up-to-the Boundary Version of Friedrichs's Lemma and Applications to the Linear Koiter Shell Model
• $L^\infty$- and $L^2$-Error Estimates for a Finite Volume Approximation of Linear Advection
• Lax theorem and finite volume schemes
• Error Estimate and the Geometric Corrector for the Upwind Finite Volume Method Applied to the Linear Advection Equation

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