Introduction to Finite Element Modelling in Geosciences
Spring Semester 2015
651-4144-00L


Lecturers:   Dave A. May (dave.may@erdw.ethz.ch)
                   Marcel Frehner (marcel.frehner@erdw.ethz.ch)


Assistants:  Mike Afanasiev, Patrick Sanan


Location:    NO building, room F11
                   Sonneggstrasse 5
                   ETH Zentrum


Dates:         July 27-31, 2015
Schedule:   9:15-13:00   14:00-17:00 (and beyond...)


Objectives:  
Learn how to program the finite element method and apply it to
equations relevant for geodynamics. The course is given in the form of
MATLAB exercises, with an introduction of the relevant theory. The
emphasis is on practical exercises, with students obtaining knowledge
of how to write their own codes.

Prerequisites:
Basic knowledge of MATLAB, linear algebra and partial differential equations.

Assessment:
The best way to ensure a mark of 6.0 is to write a 2D Stokes solver and
use it to solve a geological problem - refer to PDF below for a more
detailed break-down of the requirements.

** Requirements for assessment (2015) **

Course notes:
All theory, examples and exercises are contained in this document (PDF)

Program:
0: Motivation (presentation)

1: Basic principles
  Presentation - "Basics of the FE Method", B. Kaus, 2011
  Code - "1D FEM Matlab script"
  Additional notes - integration by parts / intgeral formula sheet
  Additional notes - more information about weak forms

2: Time for programming 1D

3: Numerical integration and isoparametric elements
  Presentation - "Numerical Integration", B. Kaus, 2011
  Presentation - "Isoparametric Elements", B. Kaus, 2011
  Additional notes - tabulated quadrature rules (Kwon & Bang)

4: Concept summary (presentation)

5: From 1D to 2D: The diffusion equation
   Additional notes - quadratic shape functions
   Example plotting routine for 2D (source)

6: Code verification
   Sample code: 1D Diffusion with manufactured solution (source)
   Sample code: Compute order of accuracy (source)

7: 2D Elasticity

8: 2D Stokes flow

Resources:
Introduction to MATLAB
MATLAB introduction scripts
Numerical modelling of rock deformation (Stefan Schmalholz, 2009)
FEM-BEM notes
The Finite Element Method, Hughes (2000)
The Finite Element Method, vol. 1, Zienkiewicz and Taylor (2000)
Finite Elements and Fast Iterative Solvers, Elman, Silvester & Wathan (2005)