On approximation in the fictitious domain method for a bidimensional transport equation |
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Authors: | Olga Martin |
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Institution: | Department of Mathematics, University “Politehnica” of Bucharest, Splaiul Independentei 313, Bucharest, Romania |
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Abstract: | In this article a numerical method for solving a two‐dimensional transport equation in the stationary case is presented. Using the techniques of the variational calculus, we find the approximate solution for a homogeneous boundary‐value problem that corresponds to a square domain D2. Then, using the method of the fictitious domain, we extend our algorithm to a boundary value problem for a set D that has an arbitrary shape. In this approach, the initial computation domain D (called physical domain) is immersed in a square domain D2. We prove that the solution obtained by this method is a good approximation of the exact solution. The theoretical results are verified with the help of a numerical example. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 |
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Keywords: | fictitious domain method integral‐differential equation transport equation variational method |
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