A Hierarchical Preconditioner for the Mortar Finite Element Method

Mortar elements form a family of nonconforming finite element methods that are more flexible than conforming finite elements and are known to be as accurate as their conforming counterparts. A fast iterative method is developed for linear, second order elliptic equations in the plane. Our algorithm is modeled on a hierarchical basis preconditioner previously analyzed and tested, for conforming case, by Barry Smith and the second author. A complete analysis and results of numerical experiments are given for lower order mortar elements and geometrically conforming decompositions of the region into subregions.

[1]  J. H. Bramble,et al.  A second order finite difference analog of the first biharmonic boundary value problem , 1966 .

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

[3]  Olof B. Widlund,et al.  A Domain Decomposition Algorithm Using a Hierarchical Basis , 1990, SIAM J. Sci. Comput..

[4]  Barry F. Smith,et al.  Domain decomposition algorithms for the partial differential equations of linear elasticity , 1990 .

[5]  Faker Ben Belgacem.  Discrétisations 3D non conformes par la méthode de décomposition de domaine des éléments avec joints : analyse mathématique et mise en oeuvre pour le problème de Poisson , 1993 .

[6]  O. Widlund,et al.  Schwarz Methods of Neumann-Neumann Type for Three-Dimensional Elliptic Finite Element Problems , 1993 .

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

[8]  Olivier Pironneau,et al.  Substructuring preconditioners for the $Q_1$ mortar element method , 1995 .

[9]  Y. Maday,et al.  Méthode itérative de sous-structuration pour les éléments avec joints , 1996 .

[10]  Mario A. Casarin,et al.  Timely Communication: Diagonal Edge Preconditioners in p-version and Spectral Element Methods , 1997, SIAM J. Sci. Comput..

[11]  Iterative Substructuring Preconditioners for the Mortar FiniteElement Method in Two DimensionsY , 1997 .

[12]  Yvon Maday,et al.  The mortar element method for three dimensional finite elements , 1997 .