Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes

Cite Details

Konstantin Lipnikov, Mikhail Shashkov, Daniil Svyatskiy and Yuri Vassilevski, "Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes", J. Comp. Phys. (accepted), 2007

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Abstract

We consider a nonlinear finite volume (FV) scheme for stationary diffusion equation. We prove that the scheme is monotone, i.e. it preserves positivity of analytical solutions on arbitrary triangular meshes for strongly anisotropic and heterogeneous full tensor coefficients. The scheme is extended to regular star-shaped polygonal meshes and isotropic heterogeneous coefficients.

BibTeX Entry

@article{lipnikov-2007-monotone,

author = {Konstantin Lipnikov and Mikhail Shashkov and Daniil Svyatskiy and Yuri Vassilevski},

title = {Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes},

year = {2007},

journal = {J. Comp. Phys. (accepted)}

}