Convergence of finite volume scheme for degenerate parabolic problem with zero flux boundary condition
| Autor: | Mohamed Karimou Gazibo, Boris Andreianov |
|---|---|
| Přispěvatelé: | Technische Universität Berlin (TU), Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), J. Fuhrmann, M. Ohlberger and Christian Rohde, ANR-11-JS01-0006,CoToCoLa,Thématiques actuelles en lois de conservation(2011) |
| Rok vydání: | 2014 |
| Předmět: |
Discretization
35F31 01 natural sciences Integral solution Mathematics - Analysis of PDEs FOS: Mathematics Applied mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Boundary value problem Uniqueness 0101 mathematics Mathematics Dirichlet problem Finite volume method Semigroup 010102 general mathematics Degenerate energy levels Nonlinear semigroup theory Stationary problem 010101 applied mathematics Nonlinear system Finite volume scheme Degenerate parabolic problem Entropy solution [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Analysis of PDEs (math.AP) |
| Zdroj: | Springer Proceedings in Mathematics and Statistics Finite Volumes for Complex Applications VII Finite Volumes for Complex Applications VII, Jun 2014, Berlin, Germany. pp. 303-311, ⟨10.1007/978-3-319-05684-5_29⟩ Springer Proceedings in Mathematics & Statistics ISBN: 9783319056838 |
| DOI: | 10.48550/arxiv.1402.5221 |
| Popis: | This note is devoted to the study of the finite volume methods used in the discretization of degenerate parabolic-hyperbolic equation with zero-flux boundary condition. The notion of an entropy-process solution, successfully used for the Dirichlet problem, is insufficient to obtain a uniqueness and convergence result because of a lack of regularity of solutions on the boundary. We infer the uniqueness of an entropy-process solution using the tool of the nonlinear semigroup theory by passing to the new abstract notion of integral-process solution. Then, we prove that numerical solution converges to the unique entropy solution as the mesh size tends to 0. Comment: 8 |
| Databáze: | OpenAIRE |
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