MATH4981I Introduction to Finite Element Method and Finite Volume Method (3 credits)
- Description: The course introduces the construction, analysis and
applications of Finite Element Method and Finite Volume Method for
partial differential equations. Topics include finite element method
for linear elliptic equations, Godunov method and it's higher oder
extensions for linear and nonlinear hyperbolic conservation laws,
concepts of convergence, accuracy, and consistency. The course also
discusses the implementation of these algorithms using computer softwares. Students should seek
instructor's approval to take this course.
- Prerequisites: MATH3311/3312 (Previous Code: MATH230/231), MATH4351 (Previous Code: MATH331)
- Instructor: Shingyu Leung
- Email: masyleung @ ust.hk
- Office: 3491
- Office hours:
- References:
- (1) From Euler, Ritz and Galerkin to modern computing - M.J. Gander and G. Wanner
- (2) Numerical solution of partial differnetial equations - K.W. Morton and D.F. Mayers
- (3) Finite volume methods for hyperbolic problems - R.J. Leveque
Topics
- Part I: Finite Element Method
- Introduction - Reference (1)
- Linear Second Order Elliptic Equations in Two Dimensions - Reference (2) Chapter 6
- Part II: Finite Volume Method
- A) Introduction - Reference (3) Chapter 1.1-1.4
- B) Linear Equations - Reference (3)
- Chapter 2 Conservation Laws and Differential Equations
- Chapter 3 Characteristics and Riemann Problems for Linear Hyperbolic Equations
- Chapter 4 Finite Volume Methods
- Chapter 6 High Resolution Methods
- Chapter 8 Convergence, Accuracy, and Stability
- Chapter 10 Other Approaches to High Resolution
- C) Nonlinear Equations - Reference (3)
- Chapter 11 Nonlinear Scalar Conservation Laws
- Chapter 12 Finite Volume Methods for Nonlinear Scalar Conservation Laws
- Chapter 13 Nonlinear Systems of Conservation Laws
- Chapter 14 Gas Dynamics and the Euler Eqautions
- Chapter 15 Finite Volume Methods for Nonlinear Systems