Course description:
This course will focus on the Finite Element Method  (FEM) for the numerical solution of Partial Differential Equations (PDE's).
This  method is an extremely powerful tool in science and engineering  and is based on the idea of building  complicated object s(a numerical solution) using simple blocks  (elements). Some  important applications include  Structure Analysis, Elasticity, Fluid Dynamics, Electromagnetics,  Biomechanics, just to name a few.  For this introductory course we will do a blend of numerics, mathematics, and applications.

We will begin with a simple one-dimensional problem to introduce the essence of the FEM  from both the mathematical and the computational point of view.We will then study error estimates and how to use these to implement adaptive strategies.  After this, we will study different choices of FEM for Poisson's equation  in two dimensions and discuss the applicability of FEM to other linear elliptic equations.  We will end this course with a discussion on time-dependent  equations such as convection-diffusion problems and wave-like motion.

Textbook:
Most of the material will come from two books:

1. Computational Differential Equations by K. Eriksson, D.  Estep, P. Hansbo, and C. Johnson.
2. Numerical Solution of partial differential equations by the finite element method by Claes Johnson.

Programming:
You need to know how to program in either Fortran (90/95), C, C++, or Matlab and familiarize yourself with a plotting package such as Techplot, gnuplot, or  use Matlab.

Prerequisites:
No formal prerequisites, although you should be familiar with elementary linear algebra, introductory partial differential equations and numerical analysis as taught at the undergrad level. If you are unsure about the required background  come to see me.

Homework:
There will be biweekly assignments some of which will include relatively simple programming. 

Grading Policy:
Homework 100%.