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Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations


Authors: Georgios Akrivis, Buyang Li and Christian Lubich
Journal: Math. Comp. 86 (2017), 1527-1552
MSC (2010): Primary 65M12, 65M15; Secondary 65L06.
DOI: https://doi.org/10.1090/mcom/3228
Published electronically: January 9, 2017
MathSciNet review: 3626527
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Abstract: We analyze fully implicit and linearly implicit backward difference formula (BDF) methods for quasilinear parabolic equations, without making any assumptions on the growth or decay of the coefficient functions. We combine maximal parabolic regularity and energy estimates to derive optimal-order error bounds for the time-discrete approximation to the solution and its gradient in the maximum norm and energy norm.


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Additional Information

Georgios Akrivis
Affiliation: Department of Computer Science & Engineering, University of Ioannina, 451$\,$10 Ioannina, Greece
MR Author ID: 24080
Email: akrivis@cse.uoi.gr

Buyang Li
Affiliation: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
MR Author ID: 910552
Email: buyang.li@polyu.edu.hk

Christian Lubich
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle, D-72076 Tübingen, Germany
MR Author ID: 116445
Email: lubich@na.uni-tuebingen.de

Keywords: BDF methods, maximal regularity, energy technique, parabolic equations, stability, maximum norm estimates
Received by editor(s): January 26, 2016
Published electronically: January 9, 2017
Article copyright: © Copyright 2017 American Mathematical Society