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

By Barbara I. Wohlmuth. SIAM Journal on Numerical Analysis, 2000

654 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/59c6250314fb60d567da6ff0c681968da3938ba5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A formulation based on localized Lagrange multipliers for BEM–FEM coupling in contact problems (2008, methodology): “[9] solving frictionless large deformation contact problems using non-matching meshes and mortar methods, and the dual mortar method proposed by Wohlmuth [33] applied to 2D contact problems in elasticity by Flemish et al.”
Isogeometric contact analysis using mortar method (2012, methodology): “Furthermore, the mortar method was mathematically studied [27] and has been applied to various fields such as frictional contact problems [28], large deformation problems [29–31] and 3D mortar approach [32].”
Information transfer between incompatible finite element meshes: Application to coupled thermo-viscoelasticity (2006, methodology): “This connectivity can be decreased by using the dual mortar shape functions [ 40 ].”
A new dual mortar method for curved interfaces: 2D elasticity (2005, methodology): “standard ones coinciding with the trace space Wh, the dual ones spanned by piecewise linear discontinuous basis functions satisfying a biorthogonality relation with the nodal basis functions of Wh [6], the dual continuous ones where the discontinuous dual basis functions are modified by cubic polyno”
Isogeometric contact: a review (2014, background): “[105] B.”
3D fluid–structure-contact interaction based on a combined XFEM FSI and dual mortar contact approach (2010, methodology): “Moreover, they are constructed such that a biorthogonality condition as introduced in [14, 35 ,36] holds (for brevity, the discretized slave surface is denoted as � h in the following) �”
A dual mortar approach for 3D finite deformation contact with consistent linearization (2010, background): “Lagrange multiplier interpolation on the slave surface is based on so-called dual shape functions j from the discrete multiplier space Mh [13]: kh = nsl ∑ j=1 j ( (1), (1))z j , (21)”
NON-MATCHING MORTAR DISCRETIZATION ANALYSIS FOR THE COUPLING STOKES-DARCY EQUATIONS (2007, methodology): “In this paper we consider the coupling via Lagrange multipliers and we develop an analysis based on mortar finite elements techniques [4, 29] and scaled norms in order to obtain constants independent of the permeability, viscosity and ratio of mesh parameters.”
Frictionless 2D Contact formulations for finite deformations based on the mortar method (2005, methodology): “For more details regarding the mathematical analysis for linear problems, see, Wohlmuth (2000) .”
Enhanced Velocity Mixed Finite Element Methods for Flow in Multiblock Domains (2002, methodology): “The reader is referred to [6,8,13,24] and references therein for the use of mortars in the context of Galerkin finite element and finite volume methods.”
Unilateral non‐linear dynamic contact of thin‐walled structures using a primal‐dual active set strategy (2007, methodology): “The success of this strategy is based on the introduction of dual Lagrange multipliers [14] to discretize the contact pressure.”
A COMPARISON OF DUAL LAGRANGE MULTIPLIER SPACES FOR MORTAR FINITE ELEMENT DISCRETIZATIONS (2002, methodology): “Dual Lagrange multiplier spaces have been successfully introduced for low order mortar finite elements in [13].”