Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On error estimates for Galerkin spectral discretizations of parabolic problems with nonsmooth initial data
HTML articles powered by AMS MathViewer

by Javier de Frutos and Rafael Muñoz-Sola PDF
Math. Comp. 70 (2001), 525-531 Request permission


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.
  • Jöran Bergh and Jörgen Löfström, Interpolation spaces. An introduction, Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag, Berlin-New York, 1976. MR 0482275
  • Christine Bernardi and Yvon Maday, Properties of some weighted Sobolev spaces and application to spectral approximations, SIAM J. Numer. Anal. 26 (1989), no. 4, 769–829 (English, with French summary). MR 1005511, DOI 10.1137/0726045
  • Claudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni, and Thomas A. Zang, Spectral methods in fluid dynamics, Springer Series in Computational Physics, Springer-Verlag, New York, 1988. MR 917480, DOI 10.1007/978-3-642-84108-8
  • C. Canuto and A. Quarteroni, Spectral and pseudospectral methods for parabolic problems with nonperiodic boundary conditions, Calcolo 18 (1981), no. 3, 197–217. MR 647825, DOI 10.1007/BF02576357
  • Robert Dautray and Jacques-Louis Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Tome 2, Collection du Commissariat à l’Énergie Atomique: Série Scientifique. [Collection of the Atomic Energy Commission: Science Series], Masson, Paris, 1985 (French). With the collaboration of Michel Artola, Philippe Bénilan, Michel Bernadou, Michel Cessenat, Jean-Claude Nédélec, Jacques Planchard and Bruno Scheurer. MR 902801
  • J. de Frutos and R. Muñoz Sola, Chebyshev pseudospectral collocation for parabolic problems with nonconstant coefficients, Proceedings of the third international conference on spectral and high order methods, Houston (Texas), 1996, 101-107.
  • J. de Frutos and R. Muñoz Sola, Error estimates for Galerkin spectral discretizations of parabolic problems with nonsmooth data, Applied Mathematics and Computation Reports 1998/7, Universidad de Valladolid (Spain), pp. 749–754.
  • G. Fernández Manín. Algunas contribuciones al estudio del error en los métodos espectrales: optimalidad de los métodos de Jacobi y estudio del método de “patching". PhD Thesis. Santiago de Compostela, 1995.
  • A. Casal, L. Gavete, C. Conde, and J. Herranz (eds.), III Congreso de Matemática Aplicada/XIII C.E.D.Y.A. (Congreso de Ecuaciones Diferenciales y Aplicaciones), Universidad Politécnica de Madrid, Madrid, 1993 (Spanish). MR 1425638
  • P. G. Ciarlet and J.-L. Lions (eds.), Handbook of numerical analysis. Vol. II, Handbook of Numerical Analysis, II, North-Holland, Amsterdam, 1991. Finite element methods. Part 1. MR 1115235
  • Mitchell Luskin and Rolf Rannacher, On the smoothing property of the Galerkin method for parabolic equations, SIAM J. Numer. Anal. 19 (1982), no. 1, 93–113. MR 646596, DOI 10.1137/0719003
  • A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486, DOI 10.1007/978-1-4612-5561-1
  • Vidar Thomée, Galerkin finite element methods for parabolic problems, Lecture Notes in Mathematics, vol. 1054, Springer-Verlag, Berlin, 1984. MR 744045
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2000): 65M70, 65M15
  • Retrieve articles in all journals with MSC (2000): 65M70, 65M15
Additional Information
  • Javier de Frutos
  • Affiliation: Departamento de Matemática Aplicada y Computación, Universidad de Valladolid, Valladolid, Spain
  • Email:
  • Rafael Muñoz-Sola
  • Affiliation: Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, Santiago de Compostela, Spain
  • Email:
  • 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.
  • © Copyright 2000 American Mathematical Society
  • Journal: Math. Comp. 70 (2001), 525-531
  • MSC (2000): Primary 65M70, 65M15
  • DOI:
  • MathSciNet review: 1680871