Numerical Methods for Continuum Mechanics

This course is designed for students and peers who had basic classes in calculus, introduction to numerical methods, differential equations, and finite element discretizations. The goal is to provide rigorous concepts for mathematical and numerical methods for continuum mechanics problems. In these notes, these are modeled as nonstationary, nonlinear, coupled partial differential equations. A focus will be on the incompressible Navier-Stokes equations, nonlinear elasticity and their coupling resulting into fluid-structure interaction. Theory and numerics are illustrated with numerical simulations and applications.