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Error estimates for the finite element approximation of linear elastic equations in an unbounded domain


Authors: Houde Han and Weizhu Bao
Journal: Math. Comp. 70 (2001), 1437-1459
MSC (2000): Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-00-01285-0
Published electronically: October 18, 2000
MathSciNet review: 1836912
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Abstract:

In this paper we present error estimates for the finite element approximation of linear elastic equations in an unbounded domain. The finite element approximation is formulated on a bounded computational domain using a nonlocal approximate artificial boundary condition or a local one. In fact there are a family of nonlocal approximate boundary conditions with increasing accuracy (and computational cost) and a family of local ones for a given artificial boundary. Our error estimates show how the errors of the finite element approximations depend on the mesh size, the terms used in the approximate artificial boundary condition, and the location of the artificial boundary. A numerical example for Navier equations outside a circle in the plane is presented. Numerical results demonstrate the performance of our error estimates.


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Additional Information

Houde Han
Affiliation: Department of Applied Mathematics, Tsinghua University, Beijing 100084, People’s Republic of China
Email: hhan@math.tsinghua.edu.cn

Weizhu Bao
Affiliation: Department of Applied Mathematics, Tsinghua University, Beijing 100084, People’s Republic of China
Email: wbao@math.tsinghua.edu.cn

DOI: https://doi.org/10.1090/S0025-5718-00-01285-0
Keywords: Unbounded domain, finite element approximation, artificial boundary, artificial boundary condition, linear elastic equations
Received by editor(s): September 3, 1998
Received by editor(s) in revised form: September 8, 1999
Published electronically: October 18, 2000
Additional Notes: This work was supported partly by the Climbing Program of National Key Project of Foundation and the National Natural Science Foundation of China. Computation was supported by the State Key Laboratory of Scientific and Engineering Computing in China.
Article copyright: © Copyright 2000 American Mathematical Society