MAGIC100: Numerical Analysis of Partial Differential Equations

Course details

Semester

Spring 2021
Monday, January 25th to Friday, March 19th; Monday, April 26th to Friday, May 7th

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
80

Timetable

Course forum

Visit the MAGIC100 forum

Description

For course description and justification, please see Syllabus and Comments.

Prerequisites

Familiarity with basic undergraduate numerical analysis and partial differential equations are assumed.

Also, basic concepts from real analysis (Inner product space, normed spaces, Banach and Hilbert spaces) are also needed. 

Syllabus

  • Review of relevant topics from PDEs and Analysis. Motivation and showcasing of applications from various branches of mathematics. 
  •  Divided differences. Finite difference methods for parabolic and hyperbolic PDEs. 
  •  Weak derivatives and function spaces. Variational formulation of PDEs. 
  •  Galerkin projection and the construction of finite element methods for elliptic problems. 
  •  Error analysis for finite element methods. 
  •  Finite element methods for parabolic problems. 
  •  Discontinuous Galerkin methods and basic finite volume concepts for hyperbolic PDEs. 
  •  Numerical methods for nonlinear PDEs. 
  •  A brief excursion to linear and nonlinear solvers. 
  •  Applications. 

Lecturer

  • EG

    Prof Emmanuil (Manolis) Georgoulis

    University
    University of Leicester

Bibliography

No bibliography has been specified for this course.

Assessment

Coming soon

Assessment information will be available shortly.

Files

There are currently no files for this course.

Recorded Lectures

Please log in to view lecture recordings.