The finite element method with nonuniform mesh sizes for unbounded domains

Author:
C. I. Goldstein

Journal:
Math. Comp. **36** (1981), 387-404

MSC:
Primary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606503-5

MathSciNet review:
606503

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Abstract: The finite element method with nonuniform mesh sizes is employed to approximately solve elliptic boundary value problems in unbounded domains. Consider the following model problem:

*f*and

*g*are smooth functions, and

*f*has bounded support. This problem is approximately solved by introducing an artificial boundary near infinity, e.g. a sphere of sufficiently large radius

*R*. The intersection of this sphere with is denoted by and the given problem is replaced by

*R*large. This necessitates the solution of a large number of linear equations, so that this method is often not very good when a uniform mesh size

*h*is employed. It is shown that a nonuniform mesh may be introduced in such a way that optimal error estimates hold and the number of equations is bounded by with

*C*independent of

*h*and

*R*.

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DOI:
https://doi.org/10.1090/S0025-5718-1981-0606503-5

Article copyright:
© Copyright 1981
American Mathematical Society