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.
An optimal mesh generation algorithm for domains with Koch type boundaries / Cefalo, Massimo; Lancia, Maria Rosaria. - In: MATHEMATICS AND COMPUTERS IN SIMULATION. - ISSN 0378-4754. - STAMPA. - 106:(2014), pp. 133-162. [10.1016/j.matcom.2014.04.009]
An optimal mesh generation algorithm for domains with Koch type boundaries
CEFALO, Massimo
;LANCIA, Maria Rosaria
2014
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.File | Dimensione | Formato | |
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