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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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