期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 76, 期 3, 页码 488-507出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2018.04.031
关键词
Surface parabolic equation; Surface finite element method; Lumped mass method; Maximum principle; Error estimates
资金
- Excellent Doctor Innovation Program of Xinjiang University [XJUBSCX-2016006]
- Graduate Student Research Innovation Program of Xinjiang [XJGRI2015009]
- NSF of Xinjiang Province [2016D01C058, 2015211C289]
- Research Fund from Key Laboratory of Xinjiang Province [2017D04030]
- NSF of China [11671345, 11362021, 41501107]
- CAPES of Brazil [88881.068004/2014.01]
- CNPq of Brazil [300326/2012-2, 470934/2013-1]
The lumped mass method is extended to the surface finite element method for solving the surface parabolic equations. The main purpose of the proposed method is to overcome the difficulty that the surface finite element method does not guarantee the maximal principle of the surface heat equation. Optimal error estimates are given for the semidiscrete and fully-discrete schemes of the proposed method respectively. The maximum principle is shown for surface heat equations and its preservation by the lumped mass surface finite element under the Delaunay type triangulation. Moreover, some results of positivity and monotonicity are derived for nonlinear parabolic equations. Finally some numerical experiments are displayed to illustrate the validity and numerical performance of the proposed method. (C) 2018 Elsevier Ltd. All rights reserved.
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