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

DOI:
https://doi.org/10.1090/S0025-5718-06-01906-5

Published electronically:
September 28, 2006

MathSciNet review:
2261013

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Abstract | References | Similar Articles | Additional Information

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

Email:
jku@math.purdue.edu

DOI:
https://doi.org/10.1090/S0025-5718-06-01906-5

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.