On optimal interpolation triangle incidences
SIAM Journal on Scientific and Statistical Computing
Optimal triangular mesh generation by coordinate transformation
SIAM Journal on Scientific and Statistical Computing
Long and thin triangles can be good for linear interpolation
SIAM Journal on Numerical Analysis
Piecewise optimal triangulation for the approximation of scattered data in the plane
Computer Aided Geometric Design
Variational mesh adaptation: isotropy and equidistribution
Journal of Computational Physics
Are Bilinear Quadrilaterals Better Than Linear Triangles?
SIAM Journal on Scientific Computing
Variational mesh adaptation II: error estimates and monitor functions
Journal of Computational Physics
The complexity of finding small triangulations of convex 3-polytopes
Journal of Algorithms - Special issue: SODA 2000
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The question of adaptive mesh generation for approximation by splines has been studied for a number of years by various authors. The results have numerous applications in computational and discrete geometry, computer aided geometric design, finite element methods for numerical solutions of partial differential equations, image processing, and mesh generation for computer graphics, among others. In this paper we will investigate the questions regarding adaptive approximation of C^2 functions with arbitrary but fixed throughout the domain signature by multilinear splines. In particular, we will study the asymptotic behavior of the optimal error of the weighted uniform approximation by interpolating and quasi-interpolating multilinear splines.