日時: 2018年8月27日(月)15:00-
場所: 京都教育大学 A棟4階 1A402教室(いつもと会場が違います)
15:00-15:30
講演者: 奥村 真善美 氏（大阪大学大学院 情報科学研究科）
題目: A linear and structure-preserving scheme for a conservative Allen–Cahn equation with a time-dependent Lagrange multiplier
We propose a linear and structure-preserving scheme for a non-local conservative Allen– Cahn equation introduced by Rubinstein and Sternberg (1992) based on a combination of the discrete variational derivative method (DVDM) and a linearization technique. DVDM is a numerical method proposed by Furihata (2010). DVDM schemes inherit conservative or dissipative properties from the original PDEs in a discrete sense. By this approach, we obtain a nonlinear scheme in general. Then, we need some iterative solver to solve the system. This means that the computational cost is expensive. Therefore, we also use a linearization technique. The basic idea of our linearization technique is the decompositions of nonlinear terms by introducing extra time steps of numerical schemes. We expect that the proposed linear scheme is faster than the nonlinear one. In this talk, we show the stability, the existence and uniqueness of the solution for the proposed scheme, and the error estimate. We also show numerical experiments.
15:40-16:30
講演者: Hao Wu 氏（School of Mathematical Sciences, Fudan University）
題目: An introduction on the Energetic Variational Approach and its applications
In this talk, we will discuss the Energetic Variational Approach for modelling complex physical systems. This approach is based on a balance between the maximal dissipation principle and the least action principle. As a consequence, it naturally keeps the physical laws, such as the conservation of mass, energy dissipation and force balance. Then we will show its application to some well-known systems, for instance, the Cahn–Hilliard equation etc.