Newton Linearized Methods for Semilinear Parabolic Equations

Newton Linearized Methods for Semilinear Parabolic Equations

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

Dongfang Li

Boya Zhou

Dongfang Li

  1. Compact scheme for fractional diffusion-wave equation with spatial variable coefficient and delays

    Zhang, Qifeng | Liu, Lingling | Zhang, Chengjian

    Applicable Analysis, Vol. 101 (2022), Iss. 6 P.1911

    https://doi.org/10.1080/00036811.2020.1789600 [Citations: 14]
  2. Optimal a priori error estimate of relaxation-type linear finite element method for nonlinear Schrödinger equation

    Liu, Huini | Yi, Nianyu

    Journal of Computational and Applied Mathematics, Vol. 428 (2023), Iss. P.115147

    https://doi.org/10.1016/j.cam.2023.115147 [Citations: 1]