BALANCING DOMAIN DECOMPOSITION FOR MIXED FINITE-ELEMENTS

The rate of convergence of the Balancing Domain Decomposition method a pplied to the mixed finite element discretization of second-order elli ptic equations is analyzed. The Balancing Domain Decomposition method, introduced recently by Mandel, is a substructuring method that involv es at each iteration the solution of a local problem with Dirichlet da ta, a local problem with Neumann data, and a ''coarse grid'' problem t o propagate information globally and to insure the consistency of the Neumann problems. It is shown that the condition number grows at worst like the logarithm squared of the ratio of the subdomain size to the element size, in both two and three dimensions and for elements of arb itrary order. The bounds are uniform with respect to coefficient jumps of arbitrary size between subdomains. The key component of our analys is is the demonstration of an equivalence between the norm induced by the bilinear form on the interface and the H-1/2-norm of an interpolan t of the boundary data, Computational results from a message-passing p arallel implementation on an INTEL-Delta machine demonstrate the scala bility properties of the method and show almost optimal linear observe d speed-up for up to 64 processors.