Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes.(English)Zbl 1130.65113
The authors provide a non-linear finite volume scheme in order to integrate numerically the stationary diffusion equation. Compared with linear schemes, this scheme satisfies the following practical requirements: it is locally conservative, it is monotone, i.e., preserves the positivity of the differential solution, it is reliable on unstructured anisotropic meshes that could be severely distorted, it allows heterogeneous full diffusion tensors, it generates a sparse system with minimal number of non-zero entries, and eventually, it has “higher than the first order of accuracy for smooth solutions”. All these properties are underlined by some numerical experiments.
Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
Keywords:
stationary diffusion problem;full tensor coefficient;conformal simplicial mesh;non-linear finite-volume scheme;strong anisotropy;sharp gradients;polygonal meshes;numerical experimentsSoftware:
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References:
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