| SCHWARZ TYPE DOMAIN DECOMPOSITION ALGORITHMS FOR PARABOLIC EQUATIONS AND ERROR ESTIMATES |
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| 引用本文： | 芮洪兴,羊丹平. SCHWARZ TYPE DOMAIN DECOMPOSITION ALGORITHMS FOR PARABOLIC EQUATIONS AND ERROR ESTIMATES[J]. 应用数学学报(英文版), 1998, 14(3): 300-313. DOI: 10.1007/BF02677411 |
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| 作者姓名： | 芮洪兴 羊丹平 |
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| 作者单位： | Department of Mathematics，Shandong University，Jinan 250100，China |
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| 摘 要： | 1.IntroductionTheSchwarzalternatingmethodwasintroducedbyH.A.SchWarz(1870)120yearsagoasatechniqueforprovingtheexistenceofsolutionstocertainellipticproblemsdefinedonadomainofcomplicatedgeometries.Sincethenthemethodhasbeenextendedtononlinearproblemsandhasbeenproventobeasuitabledivideandconquertechniquetosolveawideclassofproblems,forinstance,see[2,3,8--10].Inthispaperweareinterestedinsolvingtheparabolicproblemsbyusingimplicitschemes,suchasbackwardEulerschemeinthetimevariable.Ateachfixedtimeleve…
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| 收稿时间： | 1995-05-10 |
Schwarz type domain decomposition algorithms for parabolic equations and error estimates |
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| Rui Hongxing,Yang Danping. Schwarz type domain decomposition algorithms for parabolic equations and error estimates[J]. Acta Mathematicae Applicatae Sinica, 1998, 14(3): 300-313. DOI: 10.1007/BF02677411 |
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| Authors: | Rui Hongxing Yang Danping |
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| Affiliation: | (1) Department of Mathematics, Shandong University, 250100 Jinan, China |
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| Abstract: | Two kinds of Schwarz type domain decomposition methods are introduced to solve thegeneral selfadjoint second order parabolic partial differential equstions, and the dependence ofconvergence rate of these algorithms on parameters of time-step and space-mesh is also analyzed.The convergence, independent of the iteration times at each time-level, of the approximate solution is proved and a priori optimal L2 error estimates are given. |
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| Keywords: | Schwarz algorithms parabolic problems finite element method error analysis |
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