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Abstract:
In this study, a multilevel correction-type goal-oriented adaptive finite element method is designed for semilinear elliptic equations. Concurrently, the corresponding convergence property is theoretically proved. In the novel goal-oriented adaptive finite element method, only a linearized primal equation and a linearized dual equation are required to be solved in each adaptive finite element space. To ensure convergence, the approximate solution of the primal equation was corrected by solving a small-scale semilinear elliptic equation after the central solving process in each adaptive finite element space. Since solving of the large-scale semilinear elliptic equations is avoided and the goal-oriented technique is absorbed, there has been a significant improvement in the solving efficiency for the goal functional of semilinear elliptic equations. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
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Source :
APPLIED NUMERICAL MATHEMATICS
ISSN: 0168-9274
Year: 2022
Volume: 172
Page: 224-241
2 . 8
JCR@2022
2 . 8 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
ESI HC Threshold:20
JCR Journal Grade:1
CAS Journal Grade:2
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: 7
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