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


Authors: Javier de Frutos and Rafael Muñoz-Sola
Journal: Math. Comp. 70 (2001), 525-531
MSC (2000): Primary 65M70, 65M15
DOI: https://doi.org/10.1090/S0025-5718-00-01195-9
Published electronically: March 1, 2000
MathSciNet review: 1680871
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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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Additional Information

Javier de Frutos
Affiliation: Departamento de Matemática Aplicada y Computación, Universidad de Valladolid, Valladolid, Spain
Email: frutos@mac.cie.uva.es

Rafael Muñoz-Sola
Affiliation: Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, Santiago de Compostela, Spain
Email: rafa@zmat.usc.es

DOI: https://doi.org/10.1090/S0025-5718-00-01195-9
Keywords: Spectral Galerkin method, parabolic equation, nonsmooth initial data
Received by editor(s): January 4, 1999
Received by editor(s) in revised form: April 6, 1999
Published electronically: March 1, 2000
Additional Notes: J. de Frutos was partially supported by project DGICYT PB95-705 and project JCyL VA52/96. R. Muñoz-Sola was partially supported by project DGICYT PB96-0952.
Article copyright: © Copyright 2000 American Mathematical Society

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