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http://hdl.handle.net/1942/27235
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DC Field | Value | Language |
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dc.contributor.author | MITRA, Koondanibha | - |
dc.contributor.author | POP, Sorin | - |
dc.date.accessioned | 2018-10-26T09:28:29Z | - |
dc.date.available | 2018-10-26T09:28:29Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | COMPUTERS & MATHEMATICS WITH APPLICATIONS, 77(6), p. 1722-1738 | - |
dc.identifier.issn | 0898-1221 | - |
dc.identifier.uri | http://hdl.handle.net/1942/27235 | - |
dc.description.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. | - |
dc.description.sponsorship | Shell and the Netherlands Organisation for Scientific Research (NWO), Netherlands through the CSER programme (project 14CSER016); Hasselt University, Belgium through the project BOF17BL04; The Research Foundation-Flanders (FWO), Belgium through the Odysseus programme (project G0G1316N) | - |
dc.language.iso | en | - |
dc.subject.other | Nonlinear diffusion problem; Linearization; Newton, Picard, L-scheme; Unconditional convergence; Stability; Richards equation | - |
dc.title | A modified L-Scheme to solve nonlinear diffusion problems | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 1738 | - |
dc.identifier.issue | 6 | - |
dc.identifier.spage | 1722 | - |
dc.identifier.volume | 77 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | Mitra, K (reprint author), Eindhoven Univ Technol, Dept Math & Comp Sci, Eindhoven, Netherlands. k.mitra@tue.nl | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.1016/j.camwa.2018.09.042 | - |
dc.identifier.isi | 000462110600021 | - |
item.fulltext | With Fulltext | - |
item.contributor | MITRA, Koondanibha | - |
item.contributor | POP, Sorin | - |
item.validation | ecoom 2020 | - |
item.fullcitation | MITRA, Koondanibha & POP, Sorin (2019) A modified L-Scheme to solve nonlinear diffusion problems. In: COMPUTERS & MATHEMATICS WITH APPLICATIONS, 77(6), p. 1722-1738. | - |
item.accessRights | Open Access | - |
crisitem.journal.issn | 0898-1221 | - |
crisitem.journal.eissn | 1873-7668 | - |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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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 |
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