On error estimates for Galerkin spectral discretizations of parabolic problems with nonsmooth initial data

We analyze the Legendre and Chebyshev spectral Galerkin semi-discretization s of a one dimensional homogeneous parabolic problem with nonconstant coeff icients. We present error estimates for both smooth and nonsmooth data. In the Chebyshev case a limit in the order of approximation is established. On the contrary, in the Legendre case we find an arbitrary high order of conv egence.