Anisotropic mesh refinement for finite element methods based on error reduction

Juan C. Aguilar, Jonathan Goodman

Research output: Contribution to journalArticle

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.

Original language English (US) 497-515 19 Journal of Computational and Applied Mathematics 193 2 https://doi.org/10.1016/j.cam.2005.05.036 Published - Sep 1 2006

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Anisotropic Mesh
Error Reduction
Mesh Refinement
Finite Element Method
Finite element method
Refinement
Degree of freedom
Interior Layer
Triangular Grid
Partial differential equations
Triangle
Partial differential equation
Numerical Solution
Finite Element
Model

Keywords

• Anisotropic refinement
• Error estimators
• Finite elements
• Triangular grids

ASJC Scopus subject areas

• Applied Mathematics
• Computational Mathematics
• Numerical Analysis

Cite this

Anisotropic mesh refinement for finite element methods based on error reduction. / Aguilar, Juan C.; Goodman, Jonathan.

In: Journal of Computational and Applied Mathematics, Vol. 193, No. 2, 01.09.2006, p. 497-515.

Research output: Contribution to journalArticle

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