WIAS Preprint No. 2913, (2022)

Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension


  • Heida, Martin
    ORCID: 0000-0002-7242-8175
  • Sikorski, Alexander
    ORCID: 0000-0001-9051-650X
  • Weber, Marcus

2020 Mathematics Subject Classification

  • 65N08 65N12 65N50 80M12


  • Elliptic, finite volume, Voronoi




We study consistency of cell-centered finite difference methods for elliptic equations with degenerate coefficients in any space dimension $dgeq2$. This results in order of convergence estimates in the natural weighted energy norm and in the weighted discrete $L^2$-norm on admissible meshes. The cells of meshes under consideration may be very irregular in size. We particularly allow the size of certain cells to remain bounded from below even in the asymptotic limit. For uniform meshes we show that the order of convergence is at least 1 in the energy semi-norm, provided the discrete and continuous solutions exist and the continuous solution has $H^2$ regularity.

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