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Volume 7,     Number 3,     Fall 1999

 

SUMMING LOGARITHMIC EXPANSIONS FOR
ELLIPTIC EQUATIONS IN MULTIPLY-
CONNECTED DOMAINS WITH SMALL HOLES
MICHÈLE S. TITCOMBE AND MICHAEL J. WARD

Abstract. Elliptic problems in a two-dimensional domain containing one or several small holes are studied asymptotically in the limit of small hole radius ε. As a result of the perturbation, the asymptotic solution to this class of problems contains an infinite logarithmic expansion in powers of -1/logε. A hybrid asymptotic-numerical technique is used to sum these infinite logarithmic expansions and to obtain close agreement with full numerical results. The technique is applied to certain steady-state linear and nonlinear diffusion problems and to a viscous flow problem in a straight pipe.

 

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