@Article{NMTMA-13-4,
author = {Li, Dongfang and Zhou, Boya and Li, Dongfang},
title = {Newton Linearized Methods for Semilinear Parabolic Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2020},
volume = {13},
number = {4},
pages = {928--945},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2019-0139},
url = {https://global-sci.com/article/90374/newton-linearized-methods-for-semilinear-parabolic-equations}
}