Year: 2020
Author: Dongfang Li, Boya Zhou, Dongfang Li
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 4 : pp. 928–945
Abstract
In this study, Newton linearized finite element methods are presented for solving semi-linear parabolic equations in two- and three-dimensions. The proposed scheme is a one-step, linearized and second-order method in temporal direction, while the usual linearized second-order schemes require at least two starting values. By using a temporal-spatial error splitting argument, the fully discrete scheme is proved to be convergent without time-step restrictions dependent on the spatial mesh size. Numerical examples are given to demonstrate the efficiency of the methods and to confirm the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2019-0139
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 4 : pp. 928–945
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Newton linearized methods unconditional convergence Galerkin FEMs semilinear parabolic equations.
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