Dual-Primal FETI Methods with Face Constraints

In this paper, an iterative substructuring method with Lagrange multipliers is considered for elliptic problems in three dimensions. The algorithm belongs to the family of dual-primal FETI methods using vertex and face average constraints. It is shown that the condition number of the dual-primal FETI method can be bounded polylogarithmically as a function of the dimension of the individual subregion problems and that the bounds are otherwise independent of the number of subdomains and the mesh size. Our bound also depends on a parameter TOL, which measures the variation of the coefficient of the elliptic problem. These results are obtained within a framework which was already used successfully to analyze other dual-primal FETI methods.