# 8MC00 - Numerical Analysis of Continua - BMT 3rd year / 1st quarter

### Contents

The course is focussed on the numerical solution (by means of a computer) of Partial Differential Equations, comprising the (convection) diffusion equation, equilibrium equations for solids and the Navier Stokes equation for fluids. The used method is the Finite Element Method. In the course the basics of the method are explained and applied to simple problems by means of a FEM code in MATLAB. The course is especially aimed at students with an interest in Biomechanics.

Specific subjects:

Solution of the one-dimensional diffusion equation by means of FEM / Weighted residual formulation / weak form / interpolation / Galerkin method /isoparametric elements /numerical integrationSolution of the one-dimensional convection diffusion equation by means of FEM / temporal discretization / spatial discretization / Peclet numberThree dimensional convection/diffusion equation / divergence theorem / isoparametric elements in 2 and 3 DShape functions and numerical integration / triangular elements / higher order elements / Gauss integrationInfinitesimal strain elasticity problemsStokes and Navier Stokes equation / incompressibility condition / mixed elements / Babushka-Brebbi condition / Newton linearization / time integration

### Learning objectives

• Students have to know, understand and apply the basic principles of The Finite Element Method.
• They need to understand the possibilities and limitations of FEM
• 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.
• They need to have an overview of the structure FEM packages and operational knowledge of: mlfem_nac.

### Lecturers

Responsible lecturer: C.W.J. (Cees) Oomens.

Co-lecturer: M.C. (Mark) van Turnhout.