A Convergence Analysis of Hopscotch Methods for Fourth Order Parabolic Equations.
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E. Jan W. ter Maten, G.L.G. Sleijpen (1986)
Numerische Mathematik
Tadeusz Styś (1981)
Karel Rektorys, Marie Ludvíková (1980)
Aplikace matematiky
When solving parabolic problems by the so-called Rothe method (see K. Rektorys, Czech. Math. J. 21 (96), 1971, 318-330 and other authors), some difficulties of theoretical nature are encountered in the case of nonhomogeneous initial and boundary conditions. As a rule, these difficulties lead to rather unnatural additional conditions imposed on the corresponding bilinear form and the initial and boundary functions. In the present paper, it is shown how to remove such additional assumptions in the...
G. Koeppe, Hans-Görg Roos, Lutz Tobiska (1987)
Commentationes Mathematicae Universitatis Carolinae
Komil Kuliev, Lars-Erik Persson (2007)
Applications of Mathematics
In this paper Rothe’s classical method is extended so that it can be used to solve some linear parabolic boundary value problems in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations are discussed and applied.
Miroslav Kolář, Michal Beneš, Daniel Ševčovič (2014)
Mathematica Bohemica
The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational studies are...
Michal Beneš, Shigetoshi Yazaki, Masato Kimura (2011)
Mathematica Bohemica
The paper presents the results of numerical solution of the Allen-Cahn equation with a non-local term. This equation originally mentioned by Rubinstein and Sternberg in 1992 is related to the mean-curvature flow with the constraint of constant volume enclosed by the evolving curve. We study this motion approximately by the mentioned PDE, generalize the problem by including anisotropy and discuss the computational results obtained.
A. Olejniczak (1987)
Applicationes Mathematicae
J.G. Verwer (1984)
Numerische Mathematik
E. Magenes, R. H. Nochetto, C. Verdi (1987)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Dieu Hung Hoang, Michal Beneš (2014)
Mathematica Bohemica
The paper is concerned with the graph formulation of forced anisotropic mean curvature flow in the context of the heteroepitaxial growth of quantum dots. The problem is generalized by including anisotropy by means of Finsler metrics. A semi-discrete numerical scheme based on the method of lines is presented. Computational results with various anisotropy settings are shown and discussed.
Gunter H. Meyer (1984)
Numerische Mathematik
Michal Beneš, Danielle Hilhorst, Rémi Weidenfeld (2004)
Banach Center Publications
A. Bermúdez, J. Durany (1987)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Rektorys, Karel (1986)
Equadiff 6
Juraj Zeman (1991)
Applications of Mathematics
The paper concerns the existence of bounded weak solutions of a anonlinear diffusion equation with nonhomogeneous mixed boundary conditions.
Jozef Kačur (1989)
Commentationes Mathematicae Universitatis Carolinae
Tunc Geveci (1988)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Asvadurov, S., Druskin, V., Moskow, S. (2007)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Slimane Adjerid, Joseph E. Flaherty (1988)
Numerische Mathematik
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