An optimal mesh generation algorithm for domains with Koch type boundaries

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.