Analysis of a Multigrid Algorithm for Mortar Element Method

Analysis of a Multigrid Algorithm for the Mortar Finite Element Method

A Multigrid Algorithm for the Mortar Finite Element Method

The objective of this paper is to develop and analyse a multigrid algorithm for the system of equations arising from the mortar nite element discretization of second order elliptic boundary value problems. In order to establish the inf-sup condition for the saddle point formulation and to motivate the subsequent treatment of the discretizations we revisit rst brieey the theoretical concept of t...

Multigrid Methods for Saddlepoint Problems Arising from Mortar Finite Element Discretizations

A multigrid algorithm for saddle point problems arising from mortar nite element discretizations is analyzed. Here, we do not require that the constraints at the interface are satissed in each smoothing step. Using mesh dependent norms for the Lagrange multiplier, suitable approximation and smoothing properties are established. A convergence rate independent of the meshsize is obtained for the ...

Multigrid for the Mortar Finite Element Method

A multigrid technique for uniformly preconditioning linear systems arising from a mortar finite element discretization of second order elliptic boundary value problems is described and analyzed. These problems are posed on domains partitioned into subdomains, each of which is independently triangulated in a multilevel fashion. The multilevel mortar finite element spaces based on such triangulat...

Multigrid on the interface for mortar mixed ®nite element methods for elliptic problems

We consider mixed ®nite element approximations of second order elliptic equations on domains that can be described as a union of subdomains or blocks. We assume that the subdomain grids are locally de®ned and need not match across the block boundaries. Specially chosen mortar ®nite element spaces are introduced on the interfaces for approximating the scalar variable (pressure). The mortars also...