Constructing A-spline weight functions for stable WEB-spline finite element methods

Abstract

Whereas traditional finite element methods use meshes to define domain geometry, weighted extended B-spline finite element methods rely on a weight function. A weight function is a smooth, strictly positive function which vanishes at the domain boundary at an appropriate rate. We describe a method for generating weight functions for a general class of domains based on A-splines. We demonstrate this approach and address the relationship between weight function quality and error in the resulting finite element solutions.