Rothe’s Method for Phase Field Problem

C. Vaz

Abstract


In this paper, a phase-field model is considered. Analysis of a time discretization for an initial-boundary value problem for this phase-field model is presented. Convergence is proved and existence, uniqueness and regularity results are derived.

References


[1] C. Beckermann, H.J. Diepers, I. Steinbach, A. Karma, X. Tong, Modeling melt convection in phase-field simulations of solidification, J. Comp.Phys.,

(1999), 468-496.

K. Deimling, “Nonlinear Functional Analysis”, Springer-Verlag, 1984.

K.H. Hoffman, L. Jiang, Optimal control a phase field model for solidification, Numer. Funct. Anal. Optimiz. 13, No. 1-2 (1992), 11-27.

O.A. Ladyzenskaja, N.N. Ural’ceva, “Linear and Quasilinear Elliptic Equations”, Academic Press, 1968.

O.A. Ladyzenskaja, V.A. Solonnikov, N.N. Ural’ceva, “Linear and Quasilinear Equations of Parabolic Type”, American Mathematical Society, Providence, 1968.

M. Marion, R. Temam, “Navier-Stokes Equations: Theory and Approximation”, Handbook of Numerical Analysis, Vol VI, 1998.

J.T. Oden, J.N. Reddy, “An Introduction to the Mathematical Theory of Finite Element”, John Wiley & Sons, 1976.

J. Simon, Compact sets in the space Lp(0, T;B). Annali di Matematica Pura ed Applicata, Serie Quarta, Tomo CXLVI, 1987, pp. 65-96.




DOI: https://doi.org/10.5540/tema.2007.08.03.0475

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.


Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

         

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia