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NOZ-SOLA Abstract. We analyze the Legendre and Chebyshev spectral Galerkin semi- discretizations of a one dimensional homogeneous parabolic problem with non- constant coecients. We present error estimates for both smooth and non- smooth data. In the Chebyshev case a limit in the order of approximation is established. On the contrary, in the Legendre case we nd an arbitrary high order of convegence.

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