An anisotropic unstructured triangular adaptive mesh algorithm based on error and error gradient information

Authors:
F. Marcuzzi;M.Morandi Cecchi;M. Venturin
Affiliations:
Dipartimento di Matematica Pura ed Applicata, Universitá degli Studi di Padova, Via Belzoni 7, 35131 Padova, Italy;Dipartimento di Matematica Pura ed Applicata, Universitá degli Studi di Padova, Via Belzoni 7, 35131 Padova, Italy;Dipartimento di Matematica Pura ed Applicata, Universitá degli Studi di Padova, Via Belzoni 7, 35131 Padova, Italy
Venue:
Mathematics and Computers in Simulation
Year:
2008

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Abstract

In this paper, an algorithm based on unstructured triangular meshes using standard refinement patterns for anisotropic adaptive meshes is presented. It consists of three main actions: anisotropic refinement, solution-weighted smoothing and patch unrefinement. Moreover, a hierarchical mesh formulation is used. The main idea is to use the error and error gradient on each mesh element to locally control the anisotropy of the mesh. The proposed algorithm is tested on interpolation and boundary-value problems with a discontinuous solution.