Numerical analysis for elliptic and parabolic differential equations
Official Course Description
New and more powerful computational techiques are continuously being developped. Engineers working with computations must be able to learn, and evaluate, new algorithms. The purpose of the course is to provide a thorough mathematical analysis of differential equations, focusing elliptic and parabolic problems. In the basic courses in numerical analysis the emphasis is put on construction och implementation of approximation methods. This course course aims to give the students an understanding of the more theoretical aspects of the subject. By using concepts and methods from functional analysis and from the rich theory about linear partial differential equations, we will discuss existence, stability and convergence for a number of common numerical methods. The approach to interpret both the differential equation and its numerical approximation within one and the same functional analytic framework gives a basic understanding for how numeric methods may be derived, and for how their performance is affected by the character of the original problem.