报告题目：FINITE ELEMENT METHODS FOR ENGINEERING PROBLEMS BASED ON PYTHON AND FENICS
报 告 人：Young Ju Lee，Texas State University
报告地点：腾讯会议
会议 ID：512 7002 7218 (Tuesday)，894 9893 3885 (Thursday)
校内联系人：贾继伟 jiajiwei@jlu.edu.cn
Abstract: The course goal is to introduce finite element methods (FEM) to solve a number of partial differential equations such as Poisson equation, heat equation and Navier-Stokes. An in-depth knowledge on FEM as well as iterative solvers such as multigrid methods will be discussed in a platform of FEniCS. The course will be maintained to provide not only algorithmic techniques but also a hands-on experience to implement the methods. After students complete the course works, they are expected to have abilities to tackle a number of partial differential equations using FEniCS.
授课日期 Date of Lecture |
课程名称（讲座题目） Name (Title) of Lecture |
授课时间 Duration (Beijing Time) |
参与人数 Number of Participants |
2021.07.27 |
Introduction to Finite Element Methods (FEMs) |
3:30pm-4:30pm |
15-20 |
2021.07.29 |
FEMs for Elliptic PDEs |
3:30pm-4:30pm |
15-20 |
2021.08.03 |
FEMs for Parabolic PDEs |
3:30pm-4:30pm |
15-20 |
2021.08.05 |
Mixed FEMs for Poisson Equation (Eq) |
3:30pm-4:30pm |
15-20 |
2021.08.10 |
Mixed FEMs for Stokes Eqs |
3:30pm-4:30pm |
15-20 |
2021.08.12 |
Mixed FEMs for Navier-Stokes Eqs |
3:30pm-4:30pm |
15-20 |
Lecture 1: We introduce a couple of physical problems, and a list of partial differential equations that will be discussed in the total of six lectures. Some basic information about finite element methods, Sobolev spaces, and FEniCS will be discussed.
Lecture 2: We study the conforming finite elements and how to apply them to solve Poisson equation. We also discuss and demonstrate their implementations using FEniCS.
Lecture 3: We extend the Lecture 2 to use the conforming finite elements to solve heat equation. We also discuss and demonstrate their implementations using FEniCS.
Lecture 4: We formulate the Poisson equation in a mixed formulation and discuss why such a formulation is useful. We study Raviart-Thomas and BDM finite elements to approximate vector unknowns. We then apply this to solve the mixed formulation of Poisson equation.
Lecture 5: We study the basic fluids dynamics equation, called the Stokes equation. This consists of two unknowns, velocity and pressure. We study how to solve this problem as an extension of Lecture 4. We then apply this to solve the Stokes equation in FEniCS framework.
Lecture 6: We discuss the Navier-Stokes equation, a full equation for Newtonian fluids motion. We first study how to handle the nonlinear term using fixed point iteration and then will solve the Navier-Stokes equation in FEniCS framework.
Introduction about the speaker：
报告人介绍：Young Ju Lee has obtained a Ph.D. in Mathematics from Penn State, is an Associate Professor of Mathematics at Texas State University. His main interest is in Applied Mathematics, in particular, in Computational Fluids Mechanics and Computational Nanotechnology. Dr. Lee's current focused research interest in reservoir simulations.
