[00874] Recent advances in the analysis and numerics for phase-field models
Session Time & Room : 2E (Aug.22, 17:40-19:20) @G606
Type : Proposal of Minisymposium
Abstract : Phase-field models are a powerful tool for studying the dynamics of phase transformations and internal structures in materials. In recent years, there have been significant advances in the analysis and numerical techniques for phase-field models. These advances range from innovative solution concepts and modelling approaches to structure inheriting numerical schemes together with adaptive mesh refinements.
These methods have led to a deeper understanding of the underlying physics and have had a wide range of applications in areas such as materials science, biology, and engineering.
[02784] Existence of weak solutions to an anisotropic electrokinetic flow model
Format : Talk at Waseda University
Author(s) :
Luisa Plato (WIAS)
Robert Lasarzik (Weierstrass Institut of Applied Analysis and Stochastics Berlin )
Dietmar Hömberg (Weierstrass Institut of Applied Analysis and Stochastics Berlin )
Abstract : In this talk the existence proof of weak solutions in three space dimensions to an anisotropic Navier—Stokes—Nernst—Planck—Poisson system is presented.
This models the electrokinetic flow induced by charged particles dissolved in a liquid crystals with constant director field. The existence proof relies on an approximating scheme and weak sequential compactness of the approximating sequence, which follows from the energy law. Weak—strong uniqueness is proven via the relative energy inequality.
[02502] Global existence for a singular nonlocal phase field system with inertial term
Format : Talk at Waseda University
Author(s) :
Shunsuke Kurima (Tokyo University of Science)
Abstract : This talk deals with a nonlocal phase field system with inertial term. Colli-Colturato (2018) have established existence of solutions to a phase field system related to the entropy balance. Also, Colli-Grasselli-Ito (2002) have proved existence for a parabolic-hyperbolic Penrose-Fife phase field system. However, singular nonlocal phase field systems with inertial term seem to be not studied yet.
The present work asserts that we can derive existence for a singular nonlocal phase field system with inertial term.
[02824] A structure-preserving scheme for the Liu-Wu model
Format : Talk at Waseda University
Author(s) :
Makoto Okumura (Konan University)
Abstract : Recently, the Cahn-Hilliard equation with new dynamical boundary conditions has been proposed by Liu and Wu. This model has characteristic conservation laws in that each mass of the interior of the domain and the boundary are conserved. In addition, the total energy dissipation law holds. In this talk, we propose a structure-preserving scheme for the Liu-Wu model that retains the conservation and dissipation laws in a discrete sense and show the mathematical and numerical results.
[02783] Analysis of an Allen--Cahn system in two scale topology optimization
Format : Talk at Waseda University
Author(s) :
Robert Lasarzik (Weierstrass Institut of Applied Analysis and Stochastics Berlin )
Dietmar Hoemberg (Weierstrass Institut of Applied Analysis and Stochastics Berlin )
Moritz Ebeling-RumpIn this talk, we consider an Allen—Cahn system with the obstacle potential that guarantees mass conservation. This equation is coupled to two linear elasticity equations and a nonlocal operator. This system emerged from an algorithm for a (Weierstrass Institut of Applied Analysis and Stochastics Berlin )
Abstract : In this talk, we consider an Allen—Cahn system with the obstacle potential that guarantees mass conservation. This equation is coupled to two linear elasticity equations and a nonlocal operator. This system emerged from an algorithm for a problem in two-scale topology optimization using the phase-field approach. We prove the existence of weak solutions for the associated inclusion and comment on different connections of the solvability concept and the numerical algorithm.
