A domain decomposition technique for Stokes problems
Applied Numerical Mathematics - Domain Decomposition
Mixed finite element methods for elliptic problems
Computer Methods in Applied Mechanics and Engineering
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A preconditioned iterative method for saddlepoint problems
SIAM Journal on Matrix Analysis and Applications
Domain decomposition algorithms with small overlap
SIAM Journal on Scientific Computing
Inexact and preconditioned Uzawa algorithms for saddle point problems
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Two-level additive Schwarz preconditioners for nonconforming finite element methods
Mathematics of Computation
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
SIAM Journal on Numerical Analysis
Preconditioning in H(div) and applications
Mathematics of Computation
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
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Recently a stable pair of finite element spaces for the mixed formulation of the plane elasticity system has been developed by Arnold and Winther. Here we construct a two-level overlapping Schwarz preconditioner for the resulting discrete system. Essentially, this reduces to finding an efficient preconditioner for the form (ċ,ċ) + (divċ, divċ) in the symmetric tensor space H(div,Ω). The main difficulty comes from the well known complexity of building preconditioners for the div operator. We solve it by taking a decomposition similar to the Helmholz decomposition. Both additive and multiplicative preconditioners are studied, and the conditioner numbers are shown to be uniform with respect to the mesh size.