The Finite Element Method in geodynamics

Welcome to the course Numerical Fluid Dynamics II (FEM in earth sciences) taught at Kiel University within the Geophysics master. The focus of this course is on learning how we can solve partial differential equations using the Finite Element Method (FEM). The Finite Element Method is one of the main numerical methods in mechanics and is also used in the popular geodynamics community code ASPECT. We will first learn about the basics before progressing towards solving several example problems ranging from heat diffusion, over reactive systems, to mantle convection. All examples will be implemented in Python.

Course content

These are the main topics:

  1. Getting started

  2. 1D Finite Differences.

  3. Introduction to the finite element method (FEM).

  4. 2D elliptical problems - heat diffusion.

  5. 2D parabolic problems - transient diffusion.

  6. Stokes flow.

Course goals

  1. Ability to solve geodynamics problems using numerical models.

  2. Knowledge of numerical techniques and of how to solve partial differential equations using numerical methods using Python

  3. Ability to understand how the popular geodynamics community codes like ASPECT “work”.

  4. Preparation to a possible MSc project in geophysical fluid dynamics.

Course format

The majority of this course will be spent in front of a computer working on exercises related to FEM and problems in marine geodynamics.

Open access!

Note that the materials for this course are open to everyone; the course is, however, taught as an on-site class for registered students at Kiel University.

Course information

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

References