A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces

  • Authors:

  • M. Oevermann;R. Klein

  • Affiliations:

  • Technische Universität Berlin, Institut für Energietechnik, Fasanenstr. 89, 10623 Berlin, Germany;Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 14, 14195 Berlin, Germany

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

We present a finite volume method for the solution of the two-dimensional elliptic equation @?.(@b(x)@?u(x))=f(x) with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz functions on Cartesian grids for the solution u(x) resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard multigrid solver. Singularities associated with vanishing partial volumes of intersected grid cells or the dual bilinear ansatz itself are removed by a two-step asymptotic approach. The method achieves second order of accuracy in the L^~ and L^2 norm.