An Domain Decomposition Method With Lagrange Multiplier Based On The Pointwise Matching Condition

In this paper we are concerned with the non-overlapping domain decomposition method with Lagrange multipiers based on a new pointwise matching condition. This method has an obvious merit that we can avoid executing complicated numerical integration in the process of calculating interface matrixes. To handle the singularity of each floating subdomain, we use a reg-ularization technique which transforms the corresponding singular problems into approximate positive definite problems. For the regularized method, one can build the interface equation of the multiplier directly by eliminating the primal variable. At first we derive an optimal error estimate of the resulting approximate solution for two kinds of applicable situations. Then we develop a simple preconditioner, which is much cheaper than the wellknown Dirichlet preconditioner. The effectiveness of the new preconditioner will be confirmed by both theoretical analyzes and numerical experiments.