Entry requirements

1TD325 Finite Element Methods or the equivalent.

Learning outcomes

To pass the course the student shall be able to

• derive important theorems in the area, and use these derivations to draw conlcusions about e.g. existence, uniqueness, and convergence;
• describe in what application areas different finite element types are useful;
• describe the idea behind algorithms presented in the course;
• formulate and implement methods presented in the course;
• use commercial software to solve application problems governed by more complicated partial differential equations, such as linear elasticity and transport problems.

Content

In this advanced course in finite element methods we consider several engineering application areas where finite element methods are frequently used, e.g. structural and fluid mechanics. In order to attack these problems we will study higher order and non-conforming finite elements,

non-linear solution techniques, stabilisation, and finite element methods for systems of partial differential equations. The course will contain a mix of theory and computation, both using self made codes and commercial software such as COMSOL Multiphysics.

The course content is abstract analysis of elliptic problems including existence of exact and approximate solution and error analysis. Different finite element types including higher order and non-conforming elements. Iterative methods (Picard and Newton) for non-linear problems . Stabilised methods for Transport problems such as Galerkin least squares. Applications in solid mechanics, e.g. linear elasticity. Other application areas such as fluid mechanics (Stokes and Navier Stokes equations) and electromagnetics (Maxwell's equations).

Instruction

Lectures, laboratory work, compulsory assignments.

Assessment

Written examination at the end of the course and compulsory assignments.