Sorry about the delays, but I'm finally finding some time to work
through old emails now.

On Thu, 21 Feb 2013, Manav Bhatia wrote:

I am now sure if I understand the concept of "elem_fixed_solution".

That's my fault.  The FEMSystem time integration APIs were
"prematurely optimized", readability really suffered, and we're going
to have to change the APIs soon anyway to enable stabilized nonlinear
mass matrices.

At the moment, in mass_residual():

elem_fixed_solution is equal to some fixed (integrator-dependent)
value of u during your timestep

elem_solution is equal to du/dt at the time of evaluation.
  
[M] = \int_\Omega w^T \du/dt d\Omega + \int_\Omega L(w)^T \tau du/dt d\Omega
 
How does the concept of elem_fixed_solution affect this situation with a mass 
matrix.

Assuming your L(w) is really L(u)(w) (e.g. due to advection velocity
depending on u) then you'll want to use elem_fixed_solution as the
input for that, or you'll want to yell at me to fix the API right now
so you can start writing to something saner.
---
Roy
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