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FEMwiki is an attempt to provide a clear, free, and complete resource for a class of very popular methods used in simulation software, Finite Element Methods (FEM). These methods are quite complex...
Bibliography
1. Arnold, DN and R Winther. "Mixed finite elements for elasticity". Numerische Mathematik. (2002) 92: 401–419 doi:10.1007/s002110100348
Here are a list of main articles about concepts surrounding finite element methods, each represents a category please put any relevant pages in their respective categories.
The assembly algorithm has been credited to many different people and has numerous forms. The heart of the algorithm is always the same, input the weak form of the PDE, the domain representation...
Bibliography
1. F Brezzi, J Douglas Jr, M Fortin, LD Marini. "Efficient rectangular mixed finite elements in two and three space variables". Mathematical Modelling and Numerical Analysis. vol. 21,...
Bibliography
1. Brezzi, Franco; Douglas, Jim, Jr.; Marini, L. D. "Two families of mixed finite elements for second order elliptic problems". Numerische Mathematik. vol 47. no. 2. June 1985....
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Table of Contents
Setting Environment Variables
Dolfin Makefile
On the cluster, there are a couple of details necessary to know how to make your code work properly. Below are some of...
Bibliography
1. Crouzeix, M and PA Raviart. "Conforming and nonconforming finite element methods for solving the stationary Stokes equations". 1973.
So, let's find out what things look like, shall we?
This category is a compilation of elements. It is intended to give a small introduction to each element and their applications.
This tutorial is intended for people who have never programmed any Finite Element Methods before, but generally know something about PDE's. We will describe things in a general framework and then...
FEMwiki is an attempt to provide a clear, free, and complete resource for a class of very popular methods used in simulation software, Finite Element Methods (FEM). These methods are quite complex...
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Table of Contents
Getting Started
Obtaining FEniCS
Installing the Software
Writing the Variational Form with FFC
Poisson Example
Stokes Example
Compiling and Using the Variational...
This set of tutorials are pretty general but there are a few specifics related to the ITTC cluster
FEniCS Introduction
Compiling FEniCS Simulations
Generating Meshes and FEniCS
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Table of Contents
Using Gmsh
Defining a geometry
Generating and view the mesh
Using the mesh in Dolfin
Commands for Example
This tutorial is intended to explain how to generated...
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Interpolation is the process of building a function to represent a series of data points.
The finite element method will build an interpolant of the PDE solution, based on the degrees of freedom...
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The Lagrange element, or nodal elment, was first defined with use of Lagrange interpolation polynomials in Courant's introduction of the finite elment method [1].
1D Lagrange elements order...
The Laplace equation is one of the most well known PDE's. It has numerous applications in a wide range of fields from basic mechanics to medical imaging.
The equation
The strong form of the...
Linear algebra is the the study of matrices and vectors.
Matrix-free assembly is the assembly algorithm without using a matrix to store the degrees of freedom.
Bibliography
1. Nedelec, JC. "Mixed finite elements in ". Numerische Mathematik. vol 35, no 3. September, 1980. pp 315-341. doi:10.1007/BF01396415
2. Nedelec, JC. "A new family of mixed finite...
This category contains well know partial differential equations (PDE).
Bibliography
1. Douglas N. Arnold, Richard S. Falk and Ragnar Winther. "Finite element exterior calculus, homological techniques, and applications". Acta Numerica , Volume 15, May 2006, pp 1-155....
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Table of Contents
The Mesh
The Finite Element and The Variational Form
The Assembly
Linear Solve
Visualization
Every FEM has a very basic structure. We need the following...
For now see the code in the files section. More explanation to come.
Why Use Python
Python is a high level scripting language that has some useful libraries for certain scientific operations.
We will be using the following libraries:
numpy
scipy
matplotlib
[more...
A vector element created for mixed problems by Raviart and Thomas
Bibliography
1. Raviart, PA and JM Thomas. "A mixed finite element method for 2-nd order elliptic problems". Mathematical Aspects...
Books
S.C. Brenner, R.L. Scott, "The Mathematical Theory of Finite Element Methods", 2nd Ed, Springer, 2002
T.J.R. Hughes, "The Finite Element Method: Linear Static and Dynamic Finite Element...
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FEniCS Introduction
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Welcome to your new site! Please read this first!
This page is just a welcome-page and you really might want to change it using the "edit" button at the bottom of this page and delete this...
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Table of Contents
Variational Methods
The Finite Element
The Matrix Equations
Finite Element Methods are methods for taking a Partial Differential Equation(PDE) from a continuous...
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