Bivariate splines on Tohǎneanu partition
The author considers piecewise polynomials (splines) on triangulations of two-dimensional real spaces. Unlike the univariate splines, there are spline spaces with different dimensions in this situation, depending on the geometry of the triangulation of the set on which the splines are defined. The author considers bivariate splines on certain partitions, with smoothness \(r\) and degree \(2r\), that span spaces of higher dimension than the lower bounds found by Schumaker. The properties of the piecewise polynomials depend on a phenomenon called supersmoothness which means a higher smoothness than expected across interior edges of the triangulation. In the article, not only the mentioned splines are considered but it is shown in which way the dimension of the spline spaces is a result of the supersmoothness.
scientific article; zbMATH DE number 6881301
scientific article