(The) mortar method for rectangular finite element with Lagrange multipliers

Abstract

The Mortar method is a new nonconforming approach to domain decomposition. 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 relation between the jump and the dual space as the Lagrange multiplier space. By using this method, we know that all basis functions of the finite-dimensional space are supported in a few elements. The non-conforming variational problem with the modified Lagrange multiplier space provides a discrete solution that satisfies optimal error estimates with restrict to natural norms.