Anisotropic mesh refinement for finite element methods based on error reduction

Authors:
Juan C. Aguilar;Jonathan B. Goodman
Affiliations:
Intituto Tecnológico Autónomo de México, Departamento de Matemáticas, México, Mexico;Courant Institute of Mathematical Sciences, New York University, New York, NY
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

In this paper, we propose an anisotropic adaptive refinement algorithm based on the finite element methods for the numerical solution of partial differential equations. In 2-D, for a given triangular grid and finite element approximating space V, we obtain information on location and direction of refinement by estimating the reduction of the error if a single degree of freedom is added to V. For our model problem the algorithm fits highly stretched triangles along an interior layer, reducing the number of degrees of freedom that a standard h-type isotropic refinement algorithm would use.