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.
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Caboussat, A., Rappaz, J. Analysis of a one-dimensional free boundary flow problem. Numer. Math. 101, 67–86 (2005). https://doi.org/10.1007/s00211-005-0619-0
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DOI: https://doi.org/10.1007/s00211-005-0619-0