FETI-DP method with mortar matching condition for nonconforming rectangular finite elements

Abstract

The Dual-Primal Finite Element Tearing and Interconnecting(FETI-DP) method is a practical and efficient domain decomposition method for the parallel solution of elliptic partial differential equations. And the mortar finite element method is a domain decomposition technique such that each subdomain can be associated with different discretization schemes and/or different rectangulars. Different discretization schemes and nonmatching triangulations across subregion boundaries are coupled together by a mortar method. The weak continuity condition at the interface is enforced an orthogonality space. We costruct FETI-DP formulation using the mortar matching condition and carry out numerical work with the nonconforming finite element in rectangular meshes with the local basis $\hat{Q} = Span{1,x,y,(x^2-{\frac{3}{5}x^4}(y^2-{\frac{3}{5}y^4}$. The convergence of optimal order in the broken energy norm is derived.