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

  • Authors:

  • K. Lipnikov;M. Shashkov;D. Svyatskiy;Yu. Vassilevski

  • Affiliations:

  • Los Alamos National Laboratory, Theoretical Division, MS B284, Los Alamos, NM 87545, USA;Los Alamos National Laboratory, Theoretical Division, MS B284, Los Alamos, NM 87545, USA;Los Alamos National Laboratory, Theoretical Division, MS B284, Los Alamos, NM 87545, USA;Institute of Numerical Mathematics, Russian Academy of Sciences, 8, Gubkina, 117333 Moscow, Russia

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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Abstract

We consider a non-linear 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.