Convergence of finite volume scheme for degenerate parabolic problem with zero flux boundary condition

Boris Andreïanov (1, 2) , Mohamed Karimou Gazibo (2)

1 TU - Technical University of Berlin / Technische Universität Berlin
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

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.

Mots clés: Degenerate parabolic problem; Stationary problem; Entropy solution; Integral solution; Nonlinear semigroup theory; Finite volume scheme

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Boris Andreïanov, Mohamed Karimou Gazibo. Convergence of finite volume scheme for degenerate parabolic problem with zero flux boundary condition. Finite Volumes for Complex Applications VII, Jun 2014, Berlin, Germany. pp. 303-311, ⟨10.1007/978-3-319-05684-5_29⟩. ⟨hal-00950142v2⟩