Convergence of exponential attractors for a finite element discretization of the Allen-Cahn equation
主题: Convergence of exponential attractors for a finite element discretization of the Allen-Cahn equation主讲人: Morgan Pierre地点: 腾讯会议83302663939时间: 2020-09-12 19:00:00组织单位: 理学院
Morgan Pierre is a professor of Universityof Poitiers, France. His research field is models of phase transition and phaseseparation, such as Allen-Cahn and Cahn-Hilliard type equations.
We consider a space semidiscretization of the Allen-Cahn equation byP1 finite elements. We build a family of exponential attractors associated tothe discretized equations which is robust as the mesh parameterhtends to 0. Asa corollary, we obtain an upper bound on the fractal dimension of the globalattractor which is independent of h.Our proof is adapted from the result ofEfendiev, Miranville and Zelik concerning the continuity of exponentialattractors under perturbation of the underlying semigroup. We will also discussthe case of a time discretization and some perspectives.