Mathematical Principles of Anisotropic Mesh Adaptation (Communications in Computational Physics, 2018)
Mesh adaptation is studied from the mesh control point of view. Twoprinciples, equidistribution and alignment, are obtained and found to be necessary andsufficient 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 positivedefinite matrix used for specifying the mesh information. A monitor function is definedbased on interpolation error in a way with which an error bound is minimized on a meshsatisfying the equidistribution and alignment conditions. Algorithms for generatingmeshes satisfying the conditions are developed and two-dimensional numerical resultsare presented.