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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.

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A posteriori error estimates for nonlinear problems. $L^r(0,T;L^\rho (\Omega ))$-error estimates for finite element discretizations of parabolic equations
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by R. Verfürth PDF
Math. Comp. 67 (1998), 1335-1360 Request permission

Abstract:

Using the abstract framework of [R. Verfürth: A posteriori error estimates for nonlinear problems. Finite element discretizations of elliptic equations. Math. Comput. 62 (206), 445 – 475 (1994)] we analyze a residual a posteriori error estimator for space-time finite element discretizations of quasilinear parabolic pdes. The estimator gives global upper and local lower bounds on the error of the numerical solution. The finite element discretizations in particular cover the so-called $\theta$-scheme, which includes the implicit and explicit Euler methods and the Crank-Nicholson scheme.
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Additional Information
  • R. Verfürth
  • Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany
  • Email: rv@silly.num1.ruhr-uni-bochum.de
  • Received by editor(s): March 21, 1995
  • Received by editor(s) in revised form: May 3, 1996, and January 3, 1997
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 1335-1360
  • MSC (1991): Primary 65N30, 65N15, 65J15, 76D05
  • DOI: https://doi.org/10.1090/S0025-5718-98-01011-4
  • MathSciNet review: 1604371