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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

Author: R. Verfürth
Journal: Math. Comp. 67 (1998), 1335-1360
MSC (1991): Primary 65N30, 65N15, 65J15, 76D05
MathSciNet review: 1604371
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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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R. Verfürth
Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany

Keywords: A posteriori error estimates; quasilinear parabolic pdes; space-time finite elements; $\theta$-scheme
Received by editor(s): March 21, 1995
Received by editor(s) in revised form: May 3, 1996, and January 3, 1997
Article copyright: © Copyright 1998 American Mathematical Society