Two different approaches for matching nonconforming grids: The Mortar Element method and the Feti Method

When using domain decomposition in a finite element framework for the approximation of second order elliptic or parabolic type problems, it has become appealing to tune the mesh of each subdomain to the local behaviour of the solution. The resulting discretization being then nonconforming, different approaches have been advocated to match the admissible discrete functions. We recall here the basics of two of them, the Mortar Element method and the Finite Element Tearing and Interconnecting (FETI) method, and aim at comparing them. The conclusion, both from the theoretical and numerical point of view, is in favor of the mortar element method.

[1]  Faker Ben Belgacem,et al.  The Mortar finite element method with Lagrange multipliers , 1999, Numerische Mathematik.

[2]  Charbel Farhat,et al.  Using a reduced number of Lagrange multipliers for assembling parallel incomplete field finite element approximations , 1992 .

[3]  C. Bernardi,et al.  A New Nonconforming Approach to Domain Decomposition : The Mortar Element Method , 1994 .

[4]  J. Périaux,et al.  Domain Decomposition Methods in Science and Engineering , 1994 .

[5]  P. Raviart,et al.  Primal hybrid finite element methods for 2nd order elliptic equations , 1977 .

[6]  François-Xavier Roux.  Méthode de décomposition de domaine a l'aide de multiplicateurs de Lagrange et application a la résolution en parallèle des équations de l'élasticité linéaire , 1989 .

[7]  Anthony T. Patera,et al.  Analysis of Iterative Methods for the Steady and Unsteady Stokes Problem: Application to Spectral Element Discretizations , 1993, SIAM J. Sci. Comput..

[8]  Abdellatif Agouzal,et al.  Une méthode d'éléments finis hybrides en décomposition de domaines , 1995 .

[9]  Marina Vidrascu,et al.  Three-dimensional domain decomposition methods with nonmatching grids and unstructured coarse solver , 1994 .

[10]  Jinchao Xu,et al.  Domain Decomposition Methods in Scientific and Engineering Computing , 1994 .

[11]  Harry Yserentant,et al.  On the multi-level splitting of finite element spaces , 1986 .

[12]  C. Farhat,et al.  A method of finite element tearing and interconnecting and its parallel solution algorithm , 1991 .

[13]  Jinchao Xu,et al.  Domain decomposition methods in scientific and engineering computing : proceedings of the Seventh International Conference on Domain Decomposition, October 27-30, 1993, The Pennsylvania State University , 1994 .