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Immersed boundary method: The existence of approximate solution of the two-dimensional heat equation

✍ Scribed by Ling Rao; Hongquan Chen

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 176 KB
Volume: 9
Category: Article
ISSN: 1468-1218
DOI: 10.1016/j.nonrwa.2006.11.006

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✦ Synopsis

This paper deals with the heat equation in which the source term involves a Dirac function and describes the elastic reaction of the immersed boundary. We analyze the existence of the approximate solution in two-dimensional case with Dirac function approximated by differentiable function. We obtain the result via finite element method, the Banach Fixed-Point Theorem and a theorem in nonlinear ordinary differential equations in abstract space.

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