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Volume 1, Issue 2
Mathematical Principles of Anisotropic Mesh Adaptation

W. Huang

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

Published online: 2006-01

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  • 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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@Article{CiCP-1-276, author = {W. Huang}, title = {Mathematical Principles of Anisotropic Mesh Adaptation}, journal = {Communications in Computational Physics}, year = {2006}, volume = {1}, number = {2}, pages = {276--310}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7958.html} }
TY - JOUR T1 - Mathematical Principles of Anisotropic Mesh Adaptation AU - W. Huang JO - Communications in Computational Physics VL - 2 SP - 276 EP - 310 PY - 2006 DA - 2006/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7958.html KW - AB -

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.

W. Huang. (2006). Mathematical Principles of Anisotropic Mesh Adaptation. Communications in Computational Physics. 1 (2). 276-310. doi:
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