Course content

Difference schemes for different types of partial differential equations. Analysis of consistency, order, stability and convergence. Solution of linear systems by iterative methods and preconditioning. Finite element method.

Learning outcome

1. Knowledge. The student understands the basic theory underlying the numerical solution of partial differential equations. The student masters error analysis of difference methods, and understands the concepts consistency, stability and convergence. The student has a basic understanding of the finite element method and iterative solution techniques for systems of equations.

2. Skills. The student is able to choose suitable methods for elliptic, parabolic and hyperbolic partial differential equations. The student is able to set up, implement and analyze discretization methods for selected partial differential equations. The student is able to design numerical experiments serving the purpose to verify if a PDE-solver is implemented correctly. The student is able to choose and apply suitable iterative methods for equation solving.

3. General competence. The student masters written and oral presentation of scientific problems and of the results obtained in the project work. The student is able to apply aquired mathematical knowledge in linear algebra and calculus to achieve the other goals of the course.

Learning methods and activities

Lectures, project, exercises seminars and/or presentations. The exercises require the use of a computer. Some of the exercises will be compulsory.

Compulsory assignments

• Exercises

Recommended previous knowledge

TMA4215 Numerical Mathematics or similar.

Course materials

Will be announced at the start of the course.