2 citations · 2 across the 6 of their papers we have counts for
6 papers
Multivariate polynomial splines on generalized oranges
Maritza Sirvent, Tatyana Sorokina, Nelly Villamizar +1
We consider spaces of multivariate splines defined on a particular type of simplicial partitions that we call (generalized) oranges. Such partitions are composed of a finite number…
An interpolated Galerkin finite element method for the Poisson equation
Tatyana Sorokina, Shangyou Zhang
When solving the Poisson equation by the finite element method, we use one degree of freedom for interpolation by the given Laplacian - the right hand side function in the partial…
Subdivision and spline spaces
Hal Schenck, Tatyana Sorokina
A standard construction in approximation theory is mesh refinement. For a simplicial or polyhedral mesh D in R^k, we study the subdivision D' obtained by subdividing a maximal cell…
Simplex Spline Bases on the Powell-Sabin 12-Split: Part II
Tom Lyche, Georg Muntingh
For the space of quintics on the Powell-Sabin 12-split of a triangle, we determine the simplex splines in and the six symmetric simplex spline bas…
Simplex Spline Bases on the Powell-Sabin 12-Split: Part I
Tom Lyche, Georg Muntingh
We review the construction and a few properties of the S-basis, a simplex spline basis for the quadratic splines on the Powell-Sabin 12-split.
Intrinsic Supermoothness
Boris Shekhtman, Tatyana Sorokina
The phenomenon, known as "supersmoothness" was first observed for bivariate splines and attributed to the polynomial nature of splines. Using only standard tools from multivatiate…