Weak coupling of solutions of first-order least-squares method

Author:
Jaeun Ku

Journal:
Math. Comp. **77** (2008), 1323-1332

MSC (2000):
Primary 65N30, 65N15

DOI:
https://doi.org/10.1090/S0025-5718-08-02062-0

Published electronically:
January 22, 2008

MathSciNet review:
2398770

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Abstract: A theoretical analysis of a first-order least-squares finite element method for second-order self-adjoint elliptic problems is presented. We investigate the coupling effect of the approximate solutions for the primary function and for the flux . We prove that the accuracy of the approximate solution for the primary function is weakly affected by the flux . That is, the bound for is dependent on , but only through the best approximation for multiplied by a factor of meshsize . Similarly, we provide that the bound for is dependent on , but only through the best approximation for multiplied by a factor of the meshsize . This weak coupling is not true for the non-selfadjoint case. We provide the numerical experiment supporting the theorems in this paper.

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Additional Information

**Jaeun Ku**

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

Address at time of publication:
Department of Mathematics, Oklahoma State University, 401 Mathematical Sciences, Stillwater, Oklahoma 74078-1058

Email:
jku@math.okstate.edu

DOI:
https://doi.org/10.1090/S0025-5718-08-02062-0

Keywords:
Least-squares,
finite element methods,
coupling

Received by editor(s):
November 20, 2006

Received by editor(s) in revised form:
April 16, 2007

Published electronically:
January 22, 2008

Additional Notes:
This research was supported in part by NSF grant DMS-0071412.

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.