Numerical methods for phase transition problems

Claudio Verdi

Displaying similar documents to “Numerical methods for phase transition problems”

Adapting meshes and time-steps for phase change problems

Ricardo H. Nochetto, Alfred Schmidt, Claudio Verdi (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We address the numerical approximation of the two-phase Stefan problem and discuss an adaptive finite element method based on rigorous a posteriori error estimation and refinement/coarsening. We also investigate how to restrict coarsening for the resulting method to be stable and convergent. We review implementation issues associated with bisection and conclude with simulations of a persistent corner singularity, for which adaptivity is an essential tool.

Optimal interface error estimates for the mean curvature flow

R. H. Nochetto, M. Paolini, C. Verdi (1994)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Computational studies of anisotropic diffuse interface model of microstructure formation in solidification

Beneš, Michal

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Approximation of crystalline dendrite growth in two space dimensions.

Schmidt, A. (1998)

Acta Mathematica Universitatis Comenianae. New Series

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Anisotropic mesh adaption: application to computational fluid dynamics

Simona Perotto (2005)

Bollettino dell'Unione Matematica Italiana

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In this communication we focus on goal-oriented anisotropic adaption techniques. Starting point has been the derivation of suitable anisotropic interpolation error estimates for piecewise linear finite elements, on triangular grids in $2 D$ . Then we have merged these interpolation estimates with the dual-based a posteriori error analysis proposed by R. Rannacher and R. Becker. As examples of this general anisotropic a posteriori analysis, elliptic, advection-diffusion-reaction and the Stokes...