Aim
The aim of the course is to provide a method for the solving of physical problems that are described by partial differential equations. The project in the course aim at giving the student an experience and theoretical understanding in solving comprehensive physical problems using the finite element method.

Knowledge and understanding
For a passing grade the student must

• understand the derivation of the finite element method for linear problems

• understand how the finite element method is applied to linear problems

• understand the differences between balance laws and constitutive laws

• understand the differences between different boundary conditions and how they are implemented

Skills and abilities
For a passing grade the student must

• be able to transform the strong form of a differential equation to the weak form

• be able to establish the finite element formulation from the weak form

• have the knowledge to write a finite element program

• be able to implement boundary conditions

Judgement and approach
For a passing grade the student must

• have the ability to analyse, to model and to simulate linear structures with the finite element method, as well as interpret the results

• have the understanding that different technical and physical problems can be modelled and simulated with the same numerical tools

Contents

• Discrete systems.

• Strong and weak formulation of differential equations.

• Approximating functions.

• Weighted residual methods and Galerkin’s method.

• Finite element formulation of heat conduction.

• Finite element formulation of elastic bodies.

• Finite element formulation of torsion and bending.

• Isoparametric elements and numerical integration.

Literature
Ottosen, N.S & Petersson, H.: Introduction to the Finite Element Method. Prentice Hall 1992.
CALFEM - A finite element toolbox to MATLAB. Studentlitteratur.
Wallin, M., Introduction to the Finite Element Method Exercises.