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Analysis of a mixed finite volume discretization of fourth order equations on general surfaces

A 2008 Preprint by Q. Du, L. Ju, and L. Tian

  • 2008:01
  • In this paper, we study a finite volume method for the numerical solution of a model fourth order partial differential equation defined on a smooth surface. The discretization is done via a surface mesh consisting of piecewise planar triangles and its dual surface polygonal tessellation. We provide an error estimate for the approximate solution under the norm on general regular meshes. Numerical experiments are carried out on various sample surfaces to verify the theoretical results. In addition, when the underlying mesh is constructed by the so-called constrained centroidal Voronoi meshes, we propose a numerically demonstrated superconvergent scheme to compute gradients more accurately.

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