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Cite Details

Daniil Svyatskiy, "Benchmark on Anisotropic Problems.Nonlinear monotone finite volume method", in Finite Volumes for Complex Applications V , pp. 935-947, 2008

Abstract

We consider a nonlinear finite volume (FV) method for stationary diffusion equation. We prove that the method is monotone, i.e. it preserves positivity of analytical solutions on arbitrary triangular meshes for strongly anisotropic and heterogeneous full tensor coefficients. The method is extended to regular star-shaped polygonal meshes and isotropic heterogeneous coefficients. The method has been developed in collaboration with K. Lipnikov, M. Shashkov and Y. Vassilevski and is based on ideas proposed by C. Le Potier.

BibTeX Entry

@inproceedings{svyatskiy-2008-FVCA5,
author = {Daniil Svyatskiy},
title = {Benchmark on Anisotropic Problems.Nonlinear monotone finite volume method},
year = {2008},
urlpdf = {http://math.lanl.gov/~dasvyat/papers/pdf/fvca5.pdf},
booktitle = {Finite Volumes for Complex Applications V },
pages = {935-947}
}