Course content

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. For the spatial discretization, emphasis will be put on state-of-the-art discretization approaches such as higher order spectral element methods, discontinuous Galerkin methods, or isogeometric methods. 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 higher order methods as well as 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. For the spatial discretization, emphasis will be put on state-of-the-art discretization approaches such as higher order spectral element methods, discontinuous Galerkin methods, or isogeometric methods. 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 higher order methods as well as 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.

The course is taught every second year, if there are enough students, next time Fall 2024. If there are few students, there will be guided self-study.

Course materials

Will be announced at the start of the course.