DOMAIN DECOMPOSITION WITH NONMATCHING GRIDS AND MIXED FORMULATION IN THE SPACES W-0(1,P)(OMEGA), W-0(1,Q)(OMEGA)

In this note, we deal with the domain decomposition method with nonmat ching grids Sor-tile Laplace operator In tile Sobolev space W-0(1,p)(O mega) for 2 < p < infinity. Expressing the problem by a mixed formulat ion, the Brezzi-Babuska theorem applies (see for example [18]), and we prove that the problem is well posed. A priori error estimates Sor La grangean finite elements of first order are given. Note that the appro ximate problem can be solved by elimination. This result(it is straigh tforwardly extended to the plane linearized elasticity model (see rema rk 4). This is important when one intents to solve plane nonlinear ela sticity problems by using the domain decomposition method with nonmatc hing grids combined with an adaptive finite element technique based on a posteriori error estimates (see [15]). Please note that tile right functional setting for slating nonlinear elasticity problems is the So bolev space W-1,W-p with 2 < p.