Schur complement preconditioning for elliptic systems of partial differential equations

S hur omplement pre onditioning for ellipti systems of partial di erential equations D. Loghin and A. J. Wathen One su essful approa h in the design of solution methods for saddle-point problems requires the eÆ ient solution of the asso iated S hur omplement problem ([26℄, [19℄). In the ase of problems arising from partial di erential equations the fa torization of the symbol of the operator an often suggest useful approximations for this problem. In this work we examine examples of pre onditioners for regular ellipti systems of partial di erential equations based on the S hur omplement of the symbol of the operator and highlight the possibilities and some of the diÆ ulties one may en ounter with this approa h.