Computational Partial Differential Equations with Finite Elements

Module code: MA7091

The mathematical models arising from countless physical and natural phenomena as well as social sciences such as economics and finance are based on Partial Differential Equations (PDEs). The solution of PDE problems of practical importance is rarely available in closed form, hence the need for accurate and reliable numerical (approximate) solutions. The aim of this module is to present the rigorous mathematical foundations as well as the computational aspects of the most widely used method for the numerical solution of (PDEs) -the Finite Element Method (FEM). Other techniques, such as finite differences (FD), will also be discussed, so as to give you a broader understanding of the subject.

A peculiarity of FEM is that they have a very strong theoretical grounding in the field of functional analysis, thus you will acquire a sound knowledge of functional spaces as well as of the proofs techniques used in Finite Element analysis. Numerical methods are designed to be implemented on the computer hence it is expected that you will become familiar with FEM programming techniques by implementing FEM throughout the module using both MatLab and freely available finite element libraries. 

Prerequisites

• MatLab