Project Topics
Here are some sample topics for your term projects. Unless mentioned otherwise,
all of the problems listed below are linear. It you would like
to work on one of these, please let me know. You are also encouraged to
choose your own topic, but would need to discuss it with me first.
I expect your choices to be finalized on or before November 1.
1. Analyze and implement a Petrov-Galerkin Method for the numerical solution
of a first order PDE (or a second-order PDE dominated by first-order effects).
2. Analyze and implement a Discontinuous Galerkin Method for the numerical solution
of a first order PDE (or a second-order PDE dominated by first-order effects).
3. Analyze and implement a a Ritz-Galerkin Method for the solution of a
boundary value problem in 1D or 2D with a symmetric operator
(i.e., solution via minimization of an appropriate functional).
4. Analyze and implement a Boundary Element Method (BEM) for the solution
of a boundary value problem in 2D.
5. Analyze and implement a Finite / Spectral Element Method for the
solution of a boundary value problem in 1D or 2D. Study convergence
of solutions using p-refinement.
6. Analyze and implement a Finite Element Method for the solution
of a boundary value problem in 3D.
7. Solve a nonlinear boundary value problem in 1D
(e.g., second-order diffusion equation with a nonlinear diffusion coefficient).
8. Analyze and implement a multiresolution wavelet-based method for the
solution of a boundary value problem in 1D with adaptive mesh refinement.
9. Analyze and implement a Finite Element Method for the solution
of a time-dependent problem in 1D or 2D (e.g., a second-order diffusion
or advection-diffusion equation).
10. Analyze and implement a mixed Finite Element Method for the solution
of a steady Stokes problem in 2D.
The deadline for submission of your project reports is
5:00 pm on December 30.
If you choose to submit your report via Email, only PDF and PostScript files
will be accepted (no MS Word *.doc files, please!).