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

Boris Andreïanov; Mohamed Karimou Gazibo

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arXiv · 1402.5221

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

Boris Andreïanov·Mohamed Karimou Gazibo

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Abstract

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.

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BibTeX RIS

Boris Andreïanov, Mohamed Karimou Gazibo. 2014-02-21. Convergence of finite volume scheme for degenerate parabolic problem with zero flux boundary condition. https://arxiv.org/abs/1402.5221

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