Schur complement preconditioning for elliptic systems of partial differential equations

Abstract

One successful approach in the design of solution methods for saddle-point problems requires the efficient solution of the associated Schur complement problem. In the case of problems arising from partial differential equations the factorization of the symbol of the operator can often suggest useful approximations for this problem. In this work we examine examples of preconditioners for regular elliptic systems of partial differential equations based on the Schur complement of the symbol of the operator and highlight the possibilities and some of the difficulties one may encounter with this approach.