MA8502 - Numerical Solution of Partial Differential Equations

About

Lessons are not given in the academic year 2019/2020

Course content

The course is taught every second year, if there are enough students, next time Fall 2020. If there are few students, there will be guided self-study.

This course will treat selected topics within analysis and application of the finite element method in computational mechanics, with particular emphasis on computational methods for incompressible fluid flow. High order spectral element methods will be used for the spatial discretization. These methods will be discussed in the context of the solution of the Poisson problem, the stady Stokes problem, and problems involving convection. The time discretization will include operator splitting methods. The treatment of general boundary conditions and deformed geometry will be discussed. Finally, efficient computation of quantities derived from the numerical solution ("outputs of interest") will be discussed.

Learning outcome

1. Knowledge.
This course will treat selected topics within analysis and application of the finite element method in computational mechanics, with particular emphasis on computational methods for incompressible fluid flow. High order spectral element methods will be used for the spatial discretization. These methods will be discussed in the context of the solution of the Poisson problem, the steady Stokes problem, and problems involving convection. The time discretization will include operator splitting methods. The treatment of general boundary conditions and deformed geometry will be discussed. Finally, efficient computation of quantities derived from the numerical solution ("outputs of interest") will be discussed.

2. Skills
The students should handle the techniques related to finite element method in computational mechanics with particular emphasis on computational methods for incompressible fluid flow. They should learn various discretization scheme and various approaches to treatment of boundary conditions and deformed geometry.

3. Competence.
The students should be able to participate in scientific discussions and conduct researches on high international level relatedto the finite element method and its applications in computational mechanics, in particular for fluid dynamics. They should be able to
participate in interdisciplinary projects involving the finite element method.




Learning methods and activities

Lectures, alternatively guided self-study. If the course registered students agree, the final exam may be given as a written exam.

Course materials

Will be announced at the start of the course.

Examination

  • * The location (room) for a written examination is published 3 days before examination date.
If more than one room is listed, you will find your room at Studentweb.