BV estimates for mortar methods in linear elasticity
نویسندگان
چکیده
This paper is concerned with the convergence of mortar methods applied to linear elasticity. We prove that the conventional meshdependent norms used in the analysis of mortar methods are bounded below by the BV norm. When combined with standard results, this bound establishes a decomposition-independent and mesh-independent proof of the convergence of mortar methods in linear elasticity. 2005 Elsevier B.V. All rights reserved.
منابع مشابه
A FETI-DP Formulation of Three Dimensional Elasticity Problems with Mortar Discretization
Abstract. In this paper, a FETI-DP formulation for the three dimensional elasticity problem on non-matching grids over a geometrically conforming subdomain partition is considered. To resolve the nonconformity of the finite elements, a mortar matching condition on the subdomain interfaces (faces) is imposed. By introducing Lagrange multipliers for the mortar matching constraints, the resulting ...
متن کاملA 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...
متن کاملFast Solving of Contact Problems on Complicated Geometries
We consider the numerical simulation of multi-body contact problems in linear elasticity. For the discretization of the transmission conditions at the interface between the bodies by means of a transfer operator nonconforming domain decomposition methods (mortar methods) are used. Here, we focus on the difficulties related to the discrete choice of the transfer operator. We explain in detail ho...
متن کاملA stabilized discontinuous mortar formulation for elastostatics and elastodynamics problems Part II: discontinuous Lagrange multipliers
In this paper, we introduce, analyze and test first and second order stabilized discontinuous two-field mortar formulations for linearized elasticity problems, following the stabilization technique of Brezzi and Marini [BM00] introduced in the scalar elliptic case for a three-field formulation. All the fundamental assumptions arising in mortar formulations are proved for our discretization proc...
متن کاملNon-conforming Domain Decomposition Method for Plate and Shell Problems
The mortar element method is an optimal domain decomposition method for the approximation of partial differential equations on non-matching grids. There already exists applications of the mortar method to Navier-Stokes, elasticity, and Maxwell problems. The aim of this paper is to provide an extension of the mortar method to plates and shells problems. We first recall the Discrete Kirchhoff Tri...
متن کامل