Two-level additive Schwarz preconditioners for nonconforming finite element methods

1996/01/01 by Susanne Brenner, Susanne C. Brenner · 3 citations
Engineering · Computer Science · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.1090/s0025-5718-96-00746-6

Abstract

Two-level additive Schwarz preconditioners are developed for the nonconforming P1 finite element approximation of scalar second-order symmetric positive definite elliptic boundary value problems, the Morley finite element approximation of the biharmonic equation, and the divergence-free nonconforming P1 finite element approximation of the stationary Stokes equations. The condition numbers of the preconditioned systems are shown to be bounded independent of mesh sizes and the number of subdomains in the case of generous overlap.

Cited by

• Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems
• Analysis of a multigrid preconditioner for Crouzeix-Raviart discretization of elliptic PDE with jump coefficient
• Quasi-optimality of the Crouzeix-Raviart FEM for p-Laplace-type problems

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