{"title":"Invariant region property of weak Galerkin method for semilinear parabolic equations","authors":"Mingze Qin, Xiuli Wang, Huifang Zhou","doi":"10.1016/j.cam.2024.116412","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we establish invariant region properties (IRPs) for the time-continuous and full-discrete weak Galerkin (WG) schemes of the semilinear parabolic equations. The scheme employs the semi-implicit scheme in the time direction and <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-<span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> WG method in the space direction, respectively. The full-discrete scheme is proved to preserve the IRP unconditionally on triangular meshes, and the optimal convergence order estimates in both <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norms are obtained for semi-discrete and full-discrete schemes. Some numerical results are presented to validate the theory of IRP and error estimates.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116412"},"PeriodicalIF":2.6000,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724006605","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
In this paper, we establish invariant region properties (IRPs) for the time-continuous and full-discrete weak Galerkin (WG) schemes of the semilinear parabolic equations. The scheme employs the semi-implicit scheme in the time direction and - WG method in the space direction, respectively. The full-discrete scheme is proved to preserve the IRP unconditionally on triangular meshes, and the optimal convergence order estimates in both and norms are obtained for semi-discrete and full-discrete schemes. Some numerical results are presented to validate the theory of IRP and error estimates.
期刊介绍：
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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