Geodesic
Mixed hybrid finite element scheme for stefan problem with prescribed convection
Lobachevskii journal of mathematics, Tome 13 (2003), pp. 15-24 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2003},
     volume = {13},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2003_13_a1/}
}
TY  - JOUR
AU  - M. A. Ignat'eva
AU  - A. V. Lapin
TI  - Mixed hybrid finite element scheme for stefan problem with prescribed convection
JO  - Lobachevskii journal of mathematics
PY  - 2003
SP  - 15
EP  - 24
VL  - 13
UR  - http://geodesic.mathdoc.fr/item/LJM_2003_13_a1/
LA  - en
ID  - LJM_2003_13_a1
ER  - 
%0 Journal Article
%A M. A. Ignat'eva
%A A. V. Lapin
%T Mixed hybrid finite element scheme for stefan problem with prescribed convection
%J Lobachevskii journal of mathematics
%D 2003
%P 15-24
%V 13
%U http://geodesic.mathdoc.fr/item/LJM_2003_13_a1/
%G en
%F LJM_2003_13_a1
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/

[1] Kuznetsov Yu. A., “Spectrally equivalent preconditioners for mixed hybrid discretizations of diffusion equations on distorted meshes”, J. Numer. Math., 11 (2003), 61–74 | DOI | MR | Zbl

[2] Louhenkilpi S., Laitinen E., Nieminen R., “Real-time simulation of heat transfer in continuous casting”, Metallurgical Trans. B, 24 (1996), 685–693 | DOI

[3] Mäkelä M., Männikkö T., Schramm H., Applications of nonsmooth optimization methods to continuous casting of steel, Rep. No 421, Math. Ins., Univ. Bayreuth, 1993, 24 pp. | Zbl

[4] Chen Z., Jiang L., “Approximation of a two phase continuous casting problem”, J. Part. Diff. Equations, 11 (1998), 59–72 | MR | Zbl

[5] Laitinen E., Lapin A., Pieskä J., “Mesh approximation and iterative solution of the continuous casting problem”, ENUMATH 99, eds. P. Neittaanmäki, T. Tiihonean and P. Tarvainen, World Scientific, Singapore, 2000, 601–617 | MR

[6] Brezzi F., Fortin M., Mixed and hybrid finite element methods, Springer Verlag, New-York, 1991 | MR | Zbl

[7] Roberts J. E., Thomas J. M., “Mixed and hybrid methods”, Numer. Anal., II (1991), 523–639 | DOI | MR | Zbl

[8] Rodrigues J. F., Yi F., “On a two-phase continuous casting Stefan problem with nonlinear flux”, Euro. J. Appl. Math., 1990, no. 1, 259–278 | MR | Zbl

[9] Rodrigues J. F., “Variational methods in the Stefan problem”, Lect. notes in math., Springer Verlag, 1994, 149–212 | MR

[10] Lions J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod Gauthier-Villars, Paris, 1969 | MR | Zbl

[11] Ciarlet P. G., Lions J. L., Handbook of numerical Analysis. Volume II: Finite element methods, Part I, Elsevier, Amsterdam, 1991, 928 pp. | MR