Commun. Comput. Phys., 1 (2006), pp. 276-310.


Mathematical Principles of Anisotropic Mesh Adaptation

Weizhang Huang 1*

1 Department of Mathematics, University of Kansas, Lawrence, KS 66045, U.S.A.

Received 8 September 2005; Accepted (in revised version) 27 November 2005

Abstract

Mesh adaptation is studied from the mesh control point of view. Two principles, equidistribution and alignment, are obtained and found to be necessary and sufficient for a complete control of the size, shape, and orientation of mesh elements. A key component in these principles is the monitor function, a symmetric and positive definite matrix used for specifying the mesh information. A monitor function is defined based on interpolation error in a way with which an error bound is minimized on a mesh satisfying the equidistribution and alignment conditions. Algorithms for generating meshes satisfying the conditions are developed and two-dimensional numerical results are presented.


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Key words: Mesh adaptation; anisotropic mesh; equidistribution; alignment; error analysis; finite element.


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Correspondence to: Weizhang Huang , Department of Mathematics, University of Kansas, Lawrence, KS 66045, U.S.A. Email: huang@math.ku.edu
† This work was supported in part by the NSF under grant DMS-0410545.
 

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