The finite element method with nonuniform mesh sizes for unbounded domains
Author:
C. I. Goldstein
Journal:
Math. Comp. 36 (1981), 387404
MSC:
Primary 65N30
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: where is the complement in (threedimensional Euclidean space) of a bounded set with smooth boundary , 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 This problem is then solved approximately by the finite element method, resulting in an approximate solution for each . In order to obtain a reasonably small error for , it is necessary to make 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:
http://dx.doi.org/10.1090/S00255718198106065035
PII:
S 00255718(1981)06065035
Article copyright:
© Copyright 1981
American Mathematical Society
