TY - JOUR
T1 - Newton Linearized Methods for Semilinear Parabolic Equations
AU - Zhou , Boya
AU - Li , Dongfang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 928
EP - 945
PY - 2020
DA - 2020/06
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0139
UR - https://global-sci.org/intro/article_detail/nmtma/16960.html
KW - Newton linearized methods, unconditional convergence, Galerkin FEMs, semilinear parabolic equations.
AB - <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>