Multigrid for the Mortar Finite Element Method

Analysis of a Multigrid Algorithm for the Mortar Finite Element Method

Stability Estimates of the Mortar Finite Element Method for 3-Dimensional Problems

This paper is concerned with the mortar finite element method for three spatial variables. The two main issues are the proof of the LBB condition based on appropriate choices of Lagrange multipliers and optimal efficiency of corresponding multigrid schemes for the whole coupled systems of equations. The implementation of the smoothing procedure also differs from that one used in the 2-dimension...

A Monotone Multigrid Solver for Two Body Contact Problems in Biomechanics

The purpose of the paper is to apply monotone multigrid methods to static and dynamic biomechanical contact problems. In space, a finite element method involving a mortar discretization of the contact conditions is used. In time, a new contact–stabilized Newmark scheme is presented. Numerical experiments for a two body Hertzian contact problem and a biomechanical application are reported.

A general framework for multigrid methods for mortar finite elements

In this paper, a general framework for the analysis of multigrid methods for mortar finite elements is considered. The numerical realization is based on the algebraic saddle point formulation arising from the discretization of second order elliptic equations on nonmatching grids. Suitable discrete Lagrange multipliers on the interface guarantee weak continuity and an optimal discretization sche...

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...