  The multi-frontal direct solver is the state-of-the-art algorithm for the
direct solution of sparse linear systems. This paper provides computational
complexity and memory usage estimates for the application of the multi-frontal
direct solver algorithm on linear systems resulting from B-spline-based
isogeometric finite elements, where the mesh is a structured grid. Specifically
we provide the estimates for systems resulting from $C^{p-1}$ polynomial
B-spline spaces and compare them to those obtained using $C^0$ spaces.
