Finite elements for Heat equation with Neumann boundary conditions.

roblem

(Heat equation with
Neumann boundary condition) Find the function
,
,
such
that
for some functions
and
.
The
is assumed to be a bounded domain with a
boundary. The
is the differentiation in the direction of the exterior normal to the
boundary. The functions
and
are assumed to satisfy compatibility conditions motivationally similar to
those of the proposition (
Parabolic
regularity 2
).