Displaying similar documents to “Convergence of the finite element method applied to an anisotropic phase-field model”

A linear extrapolation method for a general phase relaxation problem

Xun Jiang (1996)

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

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This paper examines a linear extrapolation time-discretization of a 2 ⁢ D phase relaxation model with temperature dependent convection and reaction. The model consists of a diffusion-advection PDE for temperature and an ODE with double obstacle ± 1 for phase variable. Under a stability constraint, this scheme is shown to converge with optimal orders O ⁢ τ ⁢ log ⁡ τ 1 / 2 for temperature and enthalpy, and O ⁢ τ 1 / 2 ⁢ log ⁡ τ 1 / 2 for heat flux as time-step τ ↓ 0 .

Finite elements methods for solving viscoelastic thin plates

Helena Růžičková, Alexander Ženíšek (1984)

Aplikace matematiky

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The present paper deals with numerical solution of a viscoelastic plate. The discrete problem is defined by C 1 -elements and a linear multistep method. The effect of numerical integration is studied as well. The rate of cnvergence is established. Some examples are given in the conclusion.

Γ -convergence of concentration problems

Micol Amar, Adriana Garroni (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this paper, we use Γ -convergence techniques to study the following variational problem S ε F ( Ω ) : = sup ε - 2 * ∫ Ω F ( u ) d x : ∫ Ω | ∇ u | 2 d x ≤ ε 2 , u = 0 on ∂ Ω , where 0 ≤ F ( t ) ≤ | t | 2 * , with 2 * = 2 n n - 2 , and Ω is a bounded domain of ℝ n , n ≥ 3 . We obtain a Γ -convergence result, on which one can easily read the usual concentration phenomena arising in critical growth problems. We extend the result to a non-homogeneous version of problem S ε F ( Ω ) . Finally, a second order expansion in Γ -convergence permits to identify the concentration points of the maximizing sequences,...