Optimal Triangular Mesh Generation by Coordinate Transformation
Eduardo F. D'Azevedo · SIAM Journal on Scientific and Statistical Computing · 1991
This paper presents the motivation for and construction of coordinate transformations that generate optimally efficient meshes for linear interpolation. The coordinate transformations are derived from a result in differential geometry characterizing a “flat” space. The optimality results are demonstrated for some numerical examples. Adaptive meshes produced by PLTMG [R. E. Bank, PLTMG: A Software Package for Solving Elliptic Partial Differential Equations, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990] are included for comparison. The paper concludes that coordinate transformation is a promising strategy for investigation into more complex optimal meshing problems in finite element analysis.