Null space algorithm and spanning tree in solving Darcy's equation

A Null Space algorithm is considered to solve the augmented system produced by the mixed finite element approximation of Darcy's Law. The method is based on the combination of a LU factorization technique for sparse matrices with an iterative Krylov solver. The computational efficiency of the method relies on the use of spanning trees to compute the LU factorization without fill-in and on a suitable stopping criterion for the iterative solver. We experimentally investigate its performance on a realistic set of selected application problems.