A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier

Authors:
Barbara I. Wohlmuth
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

Citing 0
Cited 21

A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems

Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
Parallel FETI algorithms for mortars

Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Numerical integrations and unit resolution multipliers for domain decomposition methods with nonmatching grids

Computing
Application of Lagrange multipliers for coupled problems in fluid and structural interactions

Computers and Structures
An a Posteriori Error Estimator for Two-Body Contact Problems on Non-Matching Meshes

Journal of Scientific Computing
Schwarz method for earthquake source dynamics

Journal of Computational Physics
A mortar based contact formulation for non-linear dynamics using dual Lagrange multipliers

Finite Elements in Analysis and Design
Over the mortar finite element method

ISTASC'08 Proceedings of the 8th conference on Systems theory and scientific computation
A scalable FETI-DP algorithm with non-penetration mortar conditions on contact interface

Journal of Computational and Applied Mathematics
Parallel FETI algorithms for mortars

Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems

Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
An enriched discontinuous Galerkin formulation for the coupling of non-conforming meshes

Finite Elements in Analysis and Design
The Equivalence of Standard and Mixed Finite Element Methods in Applications to Elasto-Acoustic Interaction

SIAM Journal on Scientific Computing
Schwarz preconditioned CG algorithm for the mortar finite element

Numerical Algorithms
Transient three-dimensional contact problems: mortar method. Mixed methods and conserving integration

Computational Mechanics
Presentation and comparison of selected algorithms for dynamic contact based on the Newmark scheme

Applied Numerical Mathematics
Frictional mortar contact for finite deformation problems with synthetic contact kinematics

Computational Mechanics
A finite element method for contact using a third medium

Computational Mechanics
A posteriori error estimates of hp-adaptive IPDG-FEM for elliptic obstacle problems

Applied Numerical Mathematics
Coupling discontinuous Galerkin discretizations using mortar finite elements for advection-diffusion-reaction problems

Computers & Mathematics with Applications
hp-adaptive IPDG/TDG-FEM for parabolic obstacle problems

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.01

Visualization

Abstract

The mortar finite element method allows the coupling of different discretization schemes and triangulations across subregion boundaries. In the original mortar approach the matching at the interface is realized by enforcing an orthogonality relation between the jump and a modified trace space which serves as a space of Lagrange multipliers. In this paper, this Lagrange multiplier space is replaced by a dual space without losing the optimality of the method. The advantage of this new approach is that the matching condition is much easier to realize. In particular, all the basis functions of the new method are supported in a few elements. The mortar map can be represented by a diagonal matrix; in the standard mortar method a linear system of equations must be solved. The problem is considered in a positive definite nonconforming variational as well as an equivalent saddle-point formulation.