8MC00 - Numerical analysis of continua

Contents

1. Solution of the one-dimensional diffusion equation by means of FEM / Weighted residual formulation / weak form / interpolation / Galerkin method /isoparametric elements /numerical integration
2. Solution of the one-dimensional convection diffusion equation by means of FEM / temporal discretization / spatial discretization / Peclet number
3. Three dimensional convection/diffusion equation / divergence theorem / isoparametric elements in 2 and 3 D
4. Shape functions and numerical integration / triangular elements / higher order elements / Gauss integration
5. Infinitesimal strain elasticity problems
6. Stokes and Navier Stokes equation / incompressibility condition / mixed elements / Babushka-Brebbi condition / Newton linearization / time integration

Learning objectives

1. Students have to know, understand and apply the basic principles of The Finite Element Method.
2. They need to understand the possibilities and limitations of FEM
3. They have to be able to write short MATLAB scripts for numerical integration, time integration, solution of nonlinear problems and problems related to interpolation and discretization.
4. They need to have an overview of the structure FEM packages and operational knowledge of: mlfem_nac.