On global and local mesh refinements by a generalized conforming bisection algorithm

Authors:
Antti Hannukainen;Sergey Korotov;Michal Kříek
Affiliations:
Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FI-02015 Espoo, Finland;BCAM - Basque Center for Applied Mathematics, Bizkaia Technology Park, Building 500, E - 48160 Derio, Basque Country, Spain;Institute of Mathematics, Academy of Sciences, itná 25, CZ-115 67 Prague 1, Czech Republic
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

We examine a generalized conforming bisection (GCB-)algorithm which allows both global and local nested refinements of the triangulations without generating hanging nodes. It is based on the notion of a mesh density function which prescribes where and how much to refine the mesh. Some regularity properties of generated sequences of refined triangulations are proved. Several numerical tests demonstrate the efficiency of the proposed bisection algorithm. It is also shown how to modify the GCB-algorithm in order to generate anisotropic meshes with high aspect ratios.