Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



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
Published electronically: January 9, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65M12, 65M15, 65L06

Retrieve articles in all journals with MSC (2010): 65M12, 65M15, 65L06

Additional Information

Georgios Akrivis
Affiliation: Department of Computer Science & Engineering, University of Ioannina, 451$$10 Ioannina, Greece

Buyang Li
Affiliation: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong

Christian Lubich
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle, D-72076 Tübingen, Germany

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

American Mathematical Society