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