A FETI-DP method for Crouzeix-Raviart finite element discretizations. (English) Zbl 1284.65182

Marcinkowski, Leszek; Rahman, Talal

Comput. Methods Appl. Math. 12, No. 1, 73-91 (2012).

Summary: This paper is concerned with the construction and analysis of a parallel preconditioner for a FETI-DP system of equations arising from the nonconforming Crouzeix-Raviart finite element discretization of a model elliptic problem of second order with discontinuous coefficients. We show that the condition number of the preconditioned problem is independent of the coefficient jumps, and grows only as \((1 + \log(H/h))^2\), where \(H\) and \(h\) are mesh parameters, in other words the preconditioner is quasi optimal.

MSC:

65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F08	Preconditioners for iterative methods

Keywords:

FETI-DP method; Crouzeix-Raviart nonconforming finite element method; domain decomposition; elliptic differential equations of second order