I have labored to develop matlab scripts to do a simple advection
diffusion equation. I would like to use these scripts to lower the
barrier on using spectral element codes, and to illustrate the method
in simple settings.  The Fortran programs might be overwhelming and
so a subset of its capabilities might be extremely useful. The scripts
include quite a bit of capabilities:

1. reading an SE grid (nodes, connectivity and boundary conditions)
2. plotting the grid in various forms
   segdraw.m, secont.m, and seconthr.m
3. initializing a flow field and tracer
   seinituvp.m
4. computing spectral element data (metric factors, mass matrices, etc.)
   semassall.m and semass.m
5. Time stepping with RK3 
   serk3step.m
6. Computing gradients and weak divergences (and hence Laplacians)
   of Spectral Element functions
   sediff.m, seweakdiv.m
7. Interpolating from the SE Gauss-Lobatto roots to any set of points.
   sehev.m, seweakdiv.m
8. compute the right hand side of an explicit advection diffusion equation
   serhs.m.

There are example grids you can use in SEOM/Grids/. The script "seadv.m"
includes a simple example of an advection diffusion equation in a circular
annulus. The initial conditions are set in seinituvp.m. You can play
around with them to make them do whatever you want.

Check the scripts out. There is quite a bit of capabilities that I wish to
provide but don't really have the time for it. Here is a simple list in
no particular order:

1. Provide capabilities to plot along 1D axis when the grid is
   rectangular, and there is no variations in the function along the
   y-axis. There is nothing like an x-y plot to see what happens.
   This mostly involves understanding the grid structure and modifying
   the file seconthr.m to do a line plot instead of contours.

2. Inject periodic Capabilities by faking a connection between the first
   edge of an element and its corresponding periodic edge on the right
   side. This is useful also for doing problem on the sphere when elements
   cross the date line. It is the same issue. There is also a file called
   seperiod.m that helps in this. It has not been activated.

3. Create simple SE-grid with matlab scripts instead of my fortran programs.
   Check out rectelem.f90 from the grid generation piece.

4. Develop the capabilities to run on a spherical grid (excluding poles as
   an initial step). This is simpler then you think and mainly affects the
   calculation of the metric factors, and the mass matrices. 
   "grep SPHERE *.F" on the fortran source file will point to where the
   changes need to take place.

5. Provide capabilities to plot grids using the matlab mapping toolbox.
   The x-y coordinates are presumed to be lon-lat in degrees. This is
   equivalent to replacing plot with mplot, and contour with mcontour

6. Develop a Helmholtz equation solver


I hope you can contribute to the development and validation of this tool
box.