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Volume 13, Issue 4
Newton Linearized Methods for Semilinear Parabolic Equations

Boya Zhou & Dongfang Li

DOI: 10.4208/nmtma.OA-2019-0139

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 928-945.

Published online: 2020-06

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  • 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.

  • Keywords

Newton linearized methods, unconditional convergence, Galerkin FEMs, semilinear parabolic equations.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

dfli@hust.edu.cn (Dongfang Li)

  • BibTex
  • RIS
  • TXT
@Article{NMTMA-13-928, author = {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 = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0139}, url = {http://global-sci.org/intro/article_detail/nmtma/16960.html} }
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 -

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.

Boya Zhou & Dongfang Li. (2020). Newton Linearized Methods for Semilinear Parabolic Equations. Numerical Mathematics: Theory, Methods and Applications. 13 (4). 928-945. doi:10.4208/nmtma.OA-2019-0139
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