A non-conforming finite element method for sub-meshing

摘要

In engineering applications, there is a constant need for solving problems using finite elements, over large and complicated domains. Such analysis is often accomplished by decomposing the global domain into several sub-domains and performing the analysis individually on each local sub-domain. The global analysis can then be realized by piecing together the information that is available from each sub-domain. Non-conforming finite elements are particularly useful in this regard. In this paper, we discuss such a technique for a model problem. We derive necessary and sufficient conditions in order for the mixed method formulation of such a non-conforming method to have a unique solution. Error estimates for the finite element solution are obtained. Finally, we present computational experiments to demonstrate that this non-conforming technique is a good candidate for finite element implementation.