Adaptivity with B-spline elements

Abstract

This paper takes a stage further the work of Kraft [1] and of Grinspun et al. [2] who used subdivision formulations to show that finite element formulation can be expressed better in terms of the basis functions used to span the space, rather than in terms of the partitioning of the domain into elements. Adaptivity is achieved not by subpartitioning the domain, but by nesting of solution spaces. This paper shows how, with B-spline elements, their approach can be further simplified: a B-spline element of any degree and in any number of dimensions can be refined independently of every other within the basis. This completely avoids the linear dependence problem, and can also give slightly more focussed adaptivity, adding extra freedom only, and exactly, where it is needed, thus reducing the solution times.