AN ELLIPTIC EQUATION IN A DOMAIN WITH PERTURBED BOUNDARY
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Date
2020
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Faculty of Mathematics and computer sciences Department of Mathematics - Option : PDEs and applications
Abstract
We consider the Laplace equation, with different boundary conditions, on a planar domain defined as a disc with a small perturbation of its boundary. First, we find an asymptotic solution in the interior of the disc using two analytical methods: separations of variables and Laplace’s formula. A third approach consists in combining the asymptotic approach with finited ifferences in polar coordinates. Some numerical examples are given at the end of this work.
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Keywords
Laplace’s equation, separation of variable, Poisson’s formula, finite difference in polar coordinates, perturbed domains