Mortar finite element methods with dual lagrange multiplier spaces in 3D

Abstract

Domain Decomposition Methods are powerful in solving partial differential equations numerically and efficiently. We focus on the Mortar Finite Element Methods among the domain decomposition methods, these are nonconforming finite element methods that allow independent discretization schemes on each subdomain in matching or nonmatching grids. The mortar condition makes constraint on global domain, and a global error can be represented by the sum of local errors. In this thesis, we investigate the dual Lagrange multiplier spaces in the interfaces. When we find an approximate solution of the given problem, nodal bases of nonmortar sides are guaranteed a locality in the interfaces with using dual spaces rather than standard mortar method. These have advantages in computation. Moreover, we investigate the conforming elements in 3D, then its dual Lagrange multiplier space can be also represented by finite elements in the interfaces.