Superconvergence analysis of adaptive finite element method based on the bubble-type mesh generation

Xiangrong Li; Weiwei Zhang; Yufeng Nie

doi:10.1016/j.aml.2019.06.034

Superconvergence analysis of adaptive finite element method based on the bubble-type mesh generation

Xiangrong Li, Weiwei Zhang, Yufeng Nie

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

This paper studies the superconvergence phenomena appearing in bubble-type adaptive finite element process. Based on a mesh condition derived from the bubble-type mesh generation, a superconvergence result of ‖u_h−u_I‖_1,Ω is obtained. Further, under the recovered gradient methods, a superconvergence estimation of bubble-type adaptive procedure is established. Theoretically, the reason behind the appearance of superconvergence in bubble-type adaptive procedure is justified.

Original language	English
Pages (from-to)	322-328
Number of pages	7
Journal	Applied Mathematics Letters
Volume	98
DOIs	https://doi.org/10.1016/j.aml.2019.06.034
State	Published - Dec 2019

Keywords

Adaptive finite element method
Mesh generation
Superconvergence

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10.1016/j.aml.2019.06.034

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title = "Superconvergence analysis of adaptive finite element method based on the bubble-type mesh generation",

abstract = "This paper studies the superconvergence phenomena appearing in bubble-type adaptive finite element process. Based on a mesh condition derived from the bubble-type mesh generation, a superconvergence result of ‖uh−uI‖1,Ω is obtained. Further, under the recovered gradient methods, a superconvergence estimation of bubble-type adaptive procedure is established. Theoretically, the reason behind the appearance of superconvergence in bubble-type adaptive procedure is justified.",

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author = "Xiangrong Li and Weiwei Zhang and Yufeng Nie",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",

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AU - Nie, Yufeng

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Y1 - 2019/12

N2 - This paper studies the superconvergence phenomena appearing in bubble-type adaptive finite element process. Based on a mesh condition derived from the bubble-type mesh generation, a superconvergence result of ‖uh−uI‖1,Ω is obtained. Further, under the recovered gradient methods, a superconvergence estimation of bubble-type adaptive procedure is established. Theoretically, the reason behind the appearance of superconvergence in bubble-type adaptive procedure is justified.

AB - This paper studies the superconvergence phenomena appearing in bubble-type adaptive finite element process. Based on a mesh condition derived from the bubble-type mesh generation, a superconvergence result of ‖uh−uI‖1,Ω is obtained. Further, under the recovered gradient methods, a superconvergence estimation of bubble-type adaptive procedure is established. Theoretically, the reason behind the appearance of superconvergence in bubble-type adaptive procedure is justified.

KW - Adaptive finite element method

KW - Mesh generation

KW - Superconvergence

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JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

Superconvergence analysis of adaptive finite element method based on the bubble-type mesh generation

Abstract

Keywords

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