Programming finite element methods with weighted B-splines

We discuss the main components of the recently developed FEMB program package, which implements finite element methods with weighted B‐splines for basic linear elliptic boundary value problems in two and three dimensions. A three‐dimensional implementation without topological restrictions has not been available before. We describe in particular the mathematical background for the recursive quadrature/cubature over boundary cells and explain how to utilize the regular data structure of uniform B‐splines efficiently. Considering the Lamé–Navier equations of linear elasticity as a typical example, we illustrate the performance of the main FEMB routines. The numerical tests confirm that, due to the new integration routines, the weighted B‐spline solvers have become considerably more efficient.