PREREQUISITE:
MATH 4320:
Advanced Calculus II
HOURS: TR 0530PM-0645PM CU-Dravo 656
INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 556-8102.
Office hours: by appointment
WWW: http://www-math.cudenver.edu/~aknyazev/
Email: aknyazev@math.cudenver.edu
TEXTBOOKS:
The Mathematical Theory of Finite Elements Methods, S. Brenner,
R. Scott
Strong Elliptic Systems and Boundary Integral Equations, Cambridge University Press, 2000, William McLean.
SUBJECT:
Theoretical foundations of finite element method for elliptic boundary value problems,
Sobolev spaces, interpolation of Sobolev spaces, variational formulation of elliptic boundary value problems,
basic error estimates, applications to elasticity, practical aspects of the finite element method.
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 formal prerequisite is Advanced Calculus, but it is
very helpfull to know
a related material from the following courses:
Applied analysis, Real Analysis, Introduction to
Finite Elements, Partial Differential Equations, Numerical Solution of Partial Differential equations, Functional Analysis.
This is the highest-level graduate class. It will require an independed work and a significant intellectual effort.
CONTENTS: The class will follow the outline below, touching on each major topic in a depth that will be determined by the pace of the class.
From "Strong Elliptic Systems and Boundary Integral Equations":
From "The Mathematical Theory of Finite Elements Methods":
Ch. 0 Basic concepts;
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.
GRADING will based on projects.