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PRECONDITIONING MIXED ELEMENT METHOD FOR NONSELFADJOINT AND INDEFINITE SECOND ORDER ELLIPTIC PROBLEMS* |
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| Authors: | Chen Jinru Chen Wenbin Institute of Computational Mathematics Scientific/Engineering Comput-ing Chinese Academy of Science Beijing PRC.Permanent Ad-dress:Mathematics Department Nanjing Normal University Nanjing PRC |
| Affiliation: | Chen Jinru Chen Wenbin Institute of Computational Mathematics and Scientific/Engineering Comput-ing,Chinese Academy of Science,Beijing 100080,PRC.Permanent Ad-dress:Mathematics Department,Nanjing Normal University,Nanjing 210097,PRC.Institute of Mathematics,Fudan University,Shanghai 200433,PRC. |
| Abstract: | In this paper, an equivalence between mixed element method and nonconforming element method for nonselfad joint and indefinite second order elliptic problems is established without using any bubble functions. It is proved that the H1 -condition number of preconditioned operator B~(-1)_h A_h is uniformly bounded and its B_h-singular values cluster in a positive finite interval, where A_h is the e-quivalent nonconforming element discretization of nonsel fad joint and indefinite second order elliptic operator A, B_h is usual nonconforming element discretization of selfad joint and positive definite second order elliptic operator B. Finally a simple V-cycle multigrid implementation of B~(-1)_h is given. |
| Keywords: | Preconditioning mixed element indefinite elliptic problems. |
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