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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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SP Science China Press

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DOI

10.1002/ciuz.19990330316

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1869-1862

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A multilevel preconditioner for the CR FEM for el

Authors: Feng Wang JinRu Chen PeiQi Huang
Publish Date: 2012/05/23
Volume: 55, Issue: 7, Pages: 1513-1526
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Abstract

In this paper we propose a multilevel preconditioner for the CrouzeixRaviart finite element approximation of secondorder elliptic partial differential equations with discontinuous coefficients Since the finite element spaces are nonnested weighted intergrid transfer operators which are stable under the weighted L 2 norm are introduced to exchange information between different meshes By analyzing the eigenvalue distribution of the preconditioned system we prove that except a few small eigenvalues all the other eigenvalues are bounded below and above nearly uniformly with respect to the jump and the mesh size As a result we get that the convergence rate of the preconditioned conjugate gradient method is quasiuniform with respect to the jump and the mesh size Numerical experiments are presented to confirm our theoretical analysis

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