1 Introduction

Examples:

• vortices in a maze
• very viscous fluid on a belt

The idea of structure-preserving discretization is opposed to standard approach

make the discretization better, capture more features and make smaller errors

in so for as the goal is

to be qualitatively correct.

This means one aims at preserving quantities like

• energy
• phase transitions
• other conserved variables

on every level of the discretization. That is: preserve structure. In order words, we do not discretize the equations but the underlying structure.