An optimal mesh generation algorithm for domains with Koch type boundaries

Massimo Cefalo and Maria Rosaria Lancia

Mathematics and Computers in Simulation (MATCOM), 2014, vol. 106, issue C, 133-162

Abstract: In this paper we propose a mesh algorithm to generate a regular and conformal family of nested triangulations for a planar domain divided into two non-convex polygonal subdomains by a prefractal Koch type interface. The presence of the interface, a polygonal curve, induces a natural triangulation in which the vertices of the prefractal are also nodes of the triangulation. In order to achieve an optimal rate of convergence of the numerical approximation a suitably refined mesh around the reentrant corners is required. This is achieved by generating a mesh compliant with the Grisvard's condition. We present the mesh algorithm and a detailed proof of the Grisvard conditions.

Keywords: Mesh algorithm; Grisvard conditions; Fractal curves; Heat flow problems (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:106:y:2014:i:c:p:133-162

DOI: 10.1016/j.matcom.2014.04.009

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