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Title: Multilevel correction adaptive finite element method for semilinear elliptic equation (English)
Author: Lin, Qun
Author: Xie, Hehu
Author: Xu, Fei
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 60
Issue: 5
Year: 2015
Pages: 527-550
Summary lang: English
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Category: math
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Summary: A type of adaptive finite element method is presented for semilinear elliptic problems based on multilevel correction scheme. The main idea of the method is to transform the semilinear elliptic equation into a sequence of linearized boundary value problems on the adaptive partitions and some semilinear elliptic problems on very low dimensional finite element spaces. Hence, solving the semilinear elliptic problem can reach almost the same efficiency as the adaptive method for the associated boundary value problem. The convergence and optimal complexity of the new scheme can be derived theoretically and demonstrated numerically. (English)
Keyword: semilinear elliptic problem
Keyword: multilevel correction
Keyword: adaptive finite element method
MSC: 35J61
MSC: 62F35
MSC: 65B99
MSC: 65N30
idZBL: Zbl 06486924
idMR: MR3396479
DOI: 10.1007/s10492-015-0110-x
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Date available: 2015-09-03T10:41:25Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/144390
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