Geodesic
Mixed hybrid finite element scheme for stefan problem with prescribed convection
Lobachevskii journal of mathematics, Tome 13 (2003), pp. 15-24

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We construct a mixed hybrid finite element scheme of lowest order for the Stefan problem with prescribed convection and suggest and investigate an iterative method for its solution. In the iterative method we use a preconditioner constructed by using “standard” finite element approximation of Laplace operator on a finer grid. The proposed approach develops the results of [1], where a spectrally equivalent preconditioner for the condensed matrix in mixed hybrid finite element approximation for linear elliptic equation was constructed.
Keywords: Mixed hybrid discretization, condensed matrices, variational inequalities, Stefan problem, iterative methods, spectrally equivalent preconditioners. 
@article{LJM_2003_13_a1,
     author = {M. A. Ignat'eva and A. V. Lapin},
     title = {Mixed hybrid finite element scheme for stefan problem with prescribed convection},
     journal = {Lobachevskii journal of mathematics},
     pages = {15--24},
     publisher = {mathdoc},
     volume = {13},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2003_13_a1/}
}
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M. A. Ignat'eva; A. V. Lapin. Mixed hybrid finite element scheme for stefan problem with prescribed convection. Lobachevskii journal of mathematics, Tome 13 (2003), pp. 15-24. http://geodesic.mathdoc.fr/item/LJM_2003_13_a1/