Trivariate polynomial splines on 3D T-meshes

Abstract

Trivariate polynomial spline spaces defined on three-dimensional (3D) T-meshes are useful tools for the finite element method. In addition to dimension formulae, explicit basis functions are constructed. The approach uses Bernstein- Bezier methods to get precise conditions on the geometry of the meshes which lead to local and stable bases. Hermite interpolation using polynomial splines on 3D T-meshes is also discussed in detail, leading to an error bound for interpolation of smooth functions.