MCNAcourses ▸ NUMN18 – autumn 2017

Course facts

URL
http://www.maths.lth.se/na/courses/NUMN18
Credits:
7,5 points
Instructors:
Eskil Hansen
Teaching Assistants
--
Grading:
G,VG
Examination:
Take home exam followed by oral exam.
Prerequisites:
see course plan

Description

Elliptic and parabolic differential equations are often encountered in engineering applications, e.g., when modeling heat flows. These problems can rarely be solved analytically and it is therefore of great interest to construct computable approximations of the solutions. 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 approximation methods.

Contents

Error estimates, convergence and stability. Existence and regularity of solutions of ordinary, elliptic and parabolic differential equations. Analysis of finite differences and the finite element method. Analysis of time-stepping methods. The interaction between the spatial and temporal discretizations. Applications of partial differential equations, such as heat conduction and diffusion-reaction processes.

Course literature (primary)

Larsson and Thomee

Course literature (secondary)

Renardy and Rogers and Brenner and Scott