MATH 7760 Fall 1997

MATHEMATICAL FOUNDATIONS OF THE FINITE ELEMENT METHOD

Jan Mandel, Department of Mathematics, University of Colorado at Denver

Overview

The objective of the class is to present the Finite Element Method for elliptic problems from a rigorous mathematical perspective. The class will cover the necessary mathematical tools. The only prerequisite is Advanced Calculus. The following courses contain related material, but they are not prerequisites: Applied analysis, Real Analysis, Introduction to Finite Elements, Partial Differential Equations, Numerical Solution of Partial Differential equations, Functional Analysis.

The course is suitable for beginning as well as advanced Math graduate students as well as for Engineering students who are interested in proofs and have the necessary Advanced Calculus or Real Analysis background.

Text

S. Brenner and R. Scott, The Mathematical Theory of Finite Elements Methods

Topics covered

Ch. 0 Basic concepts

Basics of Lebesgue integration (in addition to the book)

Ch. 1 Sobolev spaces

Ch. 2 Variational formulation of elliptic boundary value problems

Ch. 3 Construction of a finite element space

Ch. 4 Polynomial approximation theory in finite element spaces

Ch. 5 n-dimensional variational problems (except 5.8)

Selected topics from further chapters as time allows: multigrid methods, mixed finite elements, max norm estimates, interpolation of linear operators

Course structure

Exercises: Students should do as many exercises from the relevant chapters of the book as possible. Ask if you want me to work specific exercises in class.

Homeworks: There will be sets of homework problems every two to three weeks.

Exams: The midterm exam in class, final take-home.

Grading: 40% each exam, 20% homeworks

Contact

Class time and location: TR 6:55-8:10 CN 214

Instructor: Jan Mandel, CU Denver Building 640, phone 556-4475, email jmandel@math.cudenver.edu

Office hours: TR 5-6 PM