On preconditioners for mortar discretization of elliptic problems

Abstract

Abstract We consider elliptic problems with discontinuous coefficients defined on a union of two polygonal subdomains. The problems are discretized by the finite element method on non‐matching triangulation across the interface. The discrete problems are described by the mortar technique in the space with constraints (the mortar condition) and in the space without constraints using Lagrange multipliers. To solve the discrete problems Preconditioned conjugate gradient iterations are used with Neumann–Dirichlet and Neumann–Neumann preconditioners in the first case, and dual Neumann–Dirichlet and dual Neumann–Neumann (or FETI, the finite element tearing and interconnecting) in the second case. An analysis of convergence of all four of these preconditioners is given. Numerical comparison of their performance on non‐matching grids is presented. The general observation is that all preconditioners considered are very robust for the cases with the discontinuity ratio of 1000 across the interface. Copyright © 2002 John Wiley & Sons, Ltd.