Speaker 报告人：Dr. Emine Celiker
Affiliation 单位：University of Dundee，Scotland， United Kingdom
Time 时间：2023年4月25日16：00-17：00
Online 在线：Tencent 会议号：181-014-364 （Code 密码：1234）
Title 题目：Overcoming the Effects of Corner Singularities on the Solutions of Partial Differential Equations
Abstract 摘要：For the approximate solution of a second-order partial differential equation, the order of accuracy of classical finite-element or finite-difference methods depends on the exact solution’s regularity (smoothness), as well as on the order of the approximation method. When the solution domain is a non-convex polygon, the regularity of the solution in the vicinity of a corner is reduced due to local corner singularities. As a result, numerical methods with special constructions are required for approximate solutions of high accuracy. In this talk, I will firstly present the development of a problem specific difference-analytical method for the fourth order accurate solution of the boundary value problem of Laplace’s equation in polygons. Next, the construction of a more general finite-element method forthe initial-boundary value problem of the Allen-Cahn equation (a semi-linear, reaction-diffusion equation) in polygonal domains will be introduced. Numerical results will be presented to demonstrate the performance of the constructed methods.
Bio of the speaker 报告人简介：Emine Celiker is currently a Lecturer (eq. Assistant Professor) in the Division of Mathematics, University of Dundee, UK. She has a PhD in applied mathematics and computer science, in the field of numerical analysis. She is interested in the construction and analysis of novel numerical methods for thein silicoinvestigation of biological systems and problems in engineering. Her PhD focuses on the construction and theoretical justification of highly accurate combined methods, for the approximate solution of Laplace’s equation in polygonal domains. The main topics of her postdoc period are:(i)the development and analysis of efficient finite-element methods for problems in engineering, for instance acoustics and phase-field problems (modelling the movement of two immiscible states, such as oil and water) in complex geometries, and(ii)the mathematical modelling and finite element analysis of specialised hearing systems (bioacoustics).
