Numerical Solution of Partial Differential Equations Using Element Methods

The course gives an introduction to finite element methods for the numerical solution of partial differential equations. Topics include: Minimization principle, weak formulation, boundary conditions, quadrature, error analysis, stability, convergence, implementation, direct and iterative solution of the resulting algebraic systems of equations, and applications to the Poisson equation and convection-diffusion equation.

1) Knowledge: The students have knowledge about the strong and weak formulations of linear partial differential equations. The student know the mathematical foundation for the finite element method.

2) Skills: The students are able to formulate and implement FEM applied to realistic problems, in 1, 2 and 3 dimensions, including time dependent problems. They are also able to evaluate the numerical result. 3. General competence: The students gain experience with written and oral presentation of scientific problems and results.

Lectures and exercises. The grade awarded in the course is based on written school exam (75%) and works (projects) (25%).

Students are free to choose Norwegian or English for written assessments.