Lagrange multiplier based domain decomposition method with non-matching grids for time-dependent equations

Our intention in this thesis is to study one kind of non-overlapping domain decomposed finite element method systematically-a Lagrange multiplier based domain decomposition method with non-matching grids for a time-dependent problem. This method not only refers to methods defined on a decomposition of the domain consisting of a collection of mutually disjoint subdomains, but also allows discontinuity of the interior variables across the boundary of the subdomains. We apply the method to a parabolic equation, propose its semi-discrete and fully discrete finite element approximated schemes of Lagrange multiplier based DDM with non-matching grids, study their finite element solutions' existence and uniqueness, and obtain their optimal error estimate for H/sup 1/-norm and L/sup 2/-norm.