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 - <p style="text-align: justify;">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.</p>