Please use this identifier to cite or link to this item:
http://hdl.handle.net/1942/27235
Title: | A modified L-Scheme to solve nonlinear diffusion problems | Authors: | MITRA, Koondanibha POP, Sorin |
Issue Date: | 2019 | Source: | COMPUTERS & MATHEMATICS WITH APPLICATIONS, 77(6), p. 1722-1738 | Abstract: | In this work, we propose a linearization technique for solving nonlinear elliptic partial differential equations that are obtained from the time-discretization of a wide variety of nonlinear parabolic problems. The scheme is inspired by the L-scheme, which gives unconditional convergence of the linear iterations. Here we take advantage of the fact that at a particular time step, the initial guess for the iterations can be taken as the solution of the previous time step. First it is shown for quasilinear equations that have linear diffusivity that the scheme always converges, irrespective of the time step size, the spatial discretization and the degeneracy of the associated functions. Moreover, it is shown that the convergence is linear with convergence rate proportional to the time step size. Next, for the general case it is shown that the scheme converges linearly if the time step size is smaller than a certain threshold which does not depend on the mesh size, and the convergence rate is proportional to the square root of the time step size. Finally numerical results are presented that show that the scheme is at least as fast as the modified Picard scheme, faster than the L-scheme and is more stable than the Newton or the Picard scheme. | Notes: | Mitra, K (reprint author), Eindhoven Univ Technol, Dept Math & Comp Sci, Eindhoven, Netherlands. k.mitra@tue.nl | Keywords: | Nonlinear diffusion problem; Linearization; Newton, Picard, L-scheme; Unconditional convergence; Stability; Richards equation | Document URI: | http://hdl.handle.net/1942/27235 | ISSN: | 0898-1221 | e-ISSN: | 1873-7668 | DOI: | 10.1016/j.camwa.2018.09.042 | ISI #: | 000462110600021 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2020 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
UP1806.pdf | Non Peer-reviewed author version | 2.36 MB | Adobe PDF | View/Open |
1-s2.0-S0898122118305546-main.pdf Restricted Access | Published version | 904.48 kB | Adobe PDF | View/Open Request a copy |
SCOPUSTM
Citations
8
checked on Sep 3, 2020
WEB OF SCIENCETM
Citations
40
checked on Oct 13, 2024
Page view(s)
106
checked on Sep 6, 2022
Download(s)
256
checked on Sep 6, 2022
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.