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The FEM can be very efficiently used for parabolic equations.  In fact, exhaustive analysis
have been done for parabolic systems. As suggested, the method of lines (space-part by
FEM and time-part by finite differences) is the most common way of doing it.  However, there
are other ways to approach the problem.  For example, the group led by Claes Johnson at
Chalmers University, Sweden have used the so-called space-time formulation for diffusion
equations and have shown that the scheme is of higher-order accuracy (than MOL) and stable.
Refer to papers in Computer Methods in Applied Mechanics and Engineering . In these techniques,
the time-dimension is also approxmated the same way as space-dimension.

S.Shankar
Tech CAD
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