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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Domain decomposition algorithms for mixed
methods for second-order elliptic problems


Authors: Zhangxin Chen, Richard E. Ewing and Raytcho Lazarov
Journal: Math. Comp. 65 (1996), 467-490
MSC (1991): Primary {65N30, 65N22, 65F10}
MathSciNet review: 1333307
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Abstract: In this paper domain decomposition algorithms for mixed finite element methods for linear second-order elliptic problems in $\mathbb{R}^{2}$ and $\mathbb{R}^{3}$ are developed. A convergence theory for two-level and multilevel Schwarz methods applied to the algorithms under consideration is given. It is shown that the condition number of these iterative methods is bounded uniformly from above in the same manner as in the theory of domain decomposition methods for conforming and nonconforming finite element methods for the same differential problems. Numerical experiments are presented to illustrate the present techniques.


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Additional Information

Zhangxin Chen
Affiliation: Department of Mathematics and the Institute for Scientific Computation, Texas A$&$M University, College Station, TX 77843
Address at time of publication: Department of Mathematics, Box 156, Southern Methodist University, Dallas, Texas 75275-0156
Email: zchen@isc.tamu.edu

Richard E. Ewing
Affiliation: Department of Mathematics and the Institute for Scientific Computation, Texas A$&$M University, College Station, TX 77843
Email: ewing@ewing.tamu.edu

Raytcho Lazarov
Affiliation: Department of Mathematics and the Institute for Scientific Computation, Texas A$&$M University, College Station, TX 77843
Email: lazarov@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00703-X
PII: S 0025-5718(96)00703-X
Keywords: Finite element, implementation, mixed method, conforming and nonconforming methods, domain decomposition, convergence, projection of coefficient
Received by editor(s): August 2, 1994
Received by editor(s) in revised form: March 21, 1995
Additional Notes: Partly supported by the Department of Energy under contract DE-ACOS-840R21400.
Article copyright: © Copyright 1996 American Mathematical Society