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Analysis of a one-dimensional free boundary flow problem |
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| Authors: | Alexandre Caboussat Jacques Rappaz |
| Institution: | (1) Department of Mathematics, University of Houston, 4800 Calhoun Rd, Houston, Texas, 77204-3008;(2) Institut d’Analyse et Calcul Scientifique, Faculté des Sciences de Base, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland |
| Abstract: | A one-dimensional free surface problem is considered. It consists in Burgers’ equation with an additional diffusion term on a moving interval. The well-posedness of the problem is investigated and existence and uniqueness results are obtained locally in time. A semi-discretization in space with a piecewise linear finite element method is considered. A priori and a posteriori error estimates are given for the semi-discretization in space. A time splitting scheme allows to obtain numerical results in agreement with the theoretical investigations.Supported by the Swiss National Science Foundation |
| Keywords: | 65M12 65M60 35R35 |
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