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

de Frutos, Javier; Muñoz-Sola, Rafael

doi:10.1090/S0025-5718-00-01195-9

On error estimates for Galerkin spectral discretizations of parabolic problems with nonsmooth initial data
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by Javier de Frutos and Rafael Muñoz-Sola PDF

Math. Comp. 70 (2001), 525-531 Request permission

Abstract:

We analyze the Legendre and Chebyshev spectral Galerkin semidiscretizations of a one dimensional homogeneous parabolic problem with nonconstant coefficients. 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 convegence.

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