MA0379 - Numerical Solution of Elliptic Differential Equations
Catalogue Entry
This module provides an introduction to the numerical solution of elliptic differential equations using the finite element method. The module will cover the mathematical modelling of some problems in continuum mechanics, the discretization of elliptic differential equations using the finite element method, the treatment of convection-diffusion problems and methods for solving the discrete problems arising from the discretization.
Partial differential equations are the main means of providing mathematical models in science, engineering and other fields. Generally these models must be solved numerically. This course provides an introduction to numerical techniques for solving partial differential equations of elliptic type.
A number of methods are available for discretizing partial differential equations. In this module the emphasis is on the finite element method. The finite element method has been developed over the last thirty years and today it used extensively to solve problems in structural engineering, fluid mechanics and heat conduction, for example. In this module mathematical models for describing a number of physical processes will be constructed and the mathematical foundation of the finite element method will be given. Important numerical features of the finite element method will also be discussed.
A strong effort will be made to make the module as self-contained and as easily accessible as possible. A range of mathematical skills is required for this module including calculus, analysis and matrix algebra. Theorems from vector calculus that are used in the module will be introduced at the appropriate places in the course.
Semester
Spring
Lecture Times
(Academic Year 2009-10)
| Event | Day and time | Room |
|---|---|---|
| Lectures | Tuesday 13:10-14:00 | M/0.34 |
| Tuesday 14:10-15:00 | M/0.34 | |
| Wednesday 12:10-13:00 | M/0.34 | |
| Examples Lecture | Friday 14:10-15:00 (odd weeks) | M/0.34 |
Lecturer
Recommended Books
Johnson C, Numerical solution of partial differential equations by the finite element method (CUP)
Strang G and Fix G J, Analysis of the finite element method (Prentice-Hall)
Zienkiewicz O C, The finite element method (McGraw-Hill)