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 twodimensional 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 asymptoticnumerical technique is used
to sum these infinite logarithmic expansions and to obtain
close agreement with full numerical results. The technique is
applied to certain steadystate linear and nonlinear diffusion
problems and to a viscous flow problem in a straight pipe.
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