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A least-squares method for second order noncoercive elliptic partial differential equations

Author: JaEun Ku
Journal: Math. Comp. 76 (2007), 97-114
MSC (2000): Primary 65N30; Secondary 65N15
Published electronically: September 28, 2006
MathSciNet review: 2261013
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Abstract: In this paper, we consider a least-squares method proposed by Bramble, Lazarov and Pasciak (1998) which can be thought of as a stabilized Galerkin method for noncoercive problems with unique solutions. We modify their method by weakening the strength of the stabilization terms and present various new error estimates. The modified method has all the desirable properties of the original method; indeed, we shall show some theoretical properties that are not known for the original method. At the same time, our numerical experiments show an improvement of the method due to the modification.

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Additional Information

JaEun Ku
Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907-2067

Keywords: Least-squares, stabilized Galerkin method, error estimates
Received by editor(s): November 2, 2004
Received by editor(s) in revised form: July 7, 2005
Published electronically: September 28, 2006
Additional Notes: Research supported in part by NSF grant DMS-0071412.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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