  We present a spectral method for parabolic partial differential equations
with zero Dirichlet boundary conditions. The region {\Omega} for the problem is
assumed to be simply-connected and bounded, and its boundary is assumed to be a
smooth surface. An error analysis is given, showing that spectral convergence
is obtained for sufficiently smooth solution functions. Numerical examples are
given in both R^2 and R^3.

Numerical Analysis