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Title: Linearization of the finite element method for gradient flows by Newton’s method
Authors: Akrivis, G
Li, B 
Issue Date: Apr-2021
Source: IMA journal of numerical analysis, Apr. 2021, v. 41, no. 2, p. 1411-1440
Abstract: The implicit Euler scheme for nonlinear partial differential equations of gradient flows is linearized by Newton’s method, discretized in space by the finite element method. With two Newton iterations at each time level, almost optimal order convergence of the numerical solutions is established in both the Lq(Ω) and W1,q(Ω) norms. The proof is based on techniques utilizing the resolvent estimate of elliptic operators on Lq(Ω) and the maximal Lp-regularity of fully discrete finite element solutions on W−1,q(Ω)⁠.
Publisher: Oxford University Press
Journal: IMA journal of numerical analysis 
ISSN: 0272-4979
EISSN: 1464-3642
DOI: 10.1093/imanum/draa016
Rights: © The Author(s) 2020. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record Georgios Akrivis, Buyang Li, Linearization of the finite element method for gradient flows by Newton’s method, IMA Journal of Numerical Analysis, Volume 41, Issue 2, April 2021, Pages 1411–1440, is available online at: https://doi.org/10.1093/imanum/draa016.
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