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Abstract:
This paper is to introduce a type of cascadic multigrid method for coupled semilinear elliptic equations. Instead of solving the coupled semilinear elliptic equation on a very fine finite element space directly, the new scheme needs to solve a decoupled linear system by some smoothing steps on each of multilevel finite element spaces and solve a coupled semilinear elliptic equation on a coarse space. By choosing the appropriate number of smoothing steps on different finite element spaces, the corresponding optimal convergence rate and optimal computation work can be derived. Besides, the adaptive cascadic multigrid method for coupled semilinear elliptic equations and its analysis are also presented theoretically and numerically. Moreover, the requirement of bounded second order derivatives of the nonlinear term in the existing multigrid methods is reduced to the Lipschitz continuation property in the presented new scheme. Some numerical experiments are presented to validate our theoretical analysis.
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Source :
NUMERICAL ALGORITHMS
ISSN: 1017-1398
Year: 2020
Issue: 2
Volume: 83
Page: 485-510
2 . 1 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
ESI HC Threshold:46
Cited Count:
WoS CC Cited Count: 4
SCOPUS Cited Count: 4
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 1
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