Introduction to Finite Element Modelling in Geosciences
Spring Semester 2014
651-4144-00L


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


Assistants:  Xin Zhong


Location:    NO building, room F39
                   Sonneggstrasse 5
                   ETH Zentrum


Dates:         July 7-11
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, and students obtain knowledge on
how to write their own codes.

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

Exam/mark:
Students that need a mark will have to write a 2D Stokes solver and
use it to solve a geological problem - we will provide more details
during the course.

** Requirements for assessment (2014) **

Program:
0: Motivation (presentation)

1: Basic principles (handout)
  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 (handout)

3: Numerical integration and isoparametric elements (handout)
  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 (handout)
   Additional notes - quadratic shape functions
   Example plotting routine for 2D (source)

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

7: 2D Elasticiy (handout)

8: 2D Stokes (handout)

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)