A C1-C0 virtual element discretization for a sixth-order elliptic equation

被引：0

作者：

Causil, Jose ^{[1
]}

Reales, Carlos ^{[1
]}

Velasquez, Ivan ^{[2
]}

机构：

[1] Univ Cordoba, Dept Matemat, Monteria, Colombia

[2] Univ Sinu EBZ, Fac Ciencias Basicas, Monteria, Colombia

来源：

CALCOLO | 2022年 / 59卷 / 04期

关键词：

Virtual element method; Sixth-order problem; Higher-order partial differential equations; Biharmonic problem; Error estimates;

D O I：

10.1007/s10092-022-00482-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a virtual element method for the sixth-order elliptic problem with clamped and simply supported boundary conditions type. Using arguments like Ciarlet-Raviart method we introduce an auxiliary unknown w :=Delta u and we propose a weak formulation on H-2 x H-1 Sobolev space. A C-1 x C-0 virtual element discretization is proposed to approximate the solutions of the weak formulation. We also provide the convergence and error estimates results. Finally, several numerical examples illustrating the performance of the virtual element method are reported.

引用

页数：27

共 17 条

[1] A mixed finite element method for a sixth-order elliptic problem
Droniou, Jerome
Ilyas, Muhammad
Lamichhane, Bishnu P.
Wheeler, Glen E.
IMA JOURNAL OF NUMERICAL ANALYSIS, 2019, 39 (01) : 374 - 397
[2] A C1 - C0 conforming virtual element discretization for the transmission eigenvalue problem
Mora, David
Velasquez, Ivan
RESEARCH IN THE MATHEMATICAL SCIENCES, 2021, 8 (04)
[3] A C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document}–C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^0$$\end{document} virtual element discretization for a sixth-order elliptic equation
José Causil
Carlos Reales
Iván Velásquez
Calcolo, 2022, 59 (4)
[4] A C1-C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^{1}-C^{0}$$\end{document} conforming virtual element discretization for the transmission eigenvalue problem
David Mora
Iván Velásquez
Research in the Mathematical Sciences, 2021, 8 (4)
[5] A C0 virtual element method for the biharmonic eigenvalue problem
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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2021, 98 (09) : 1821 - 1833
[6] A C0-nonconforming virtual element methods for the vibration and buckling problems of thin plates
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Mora, David
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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2023, 403
[7] A C1 VIRTUAL ELEMENT METHOD FOR THE CAHN-HILLIARD EQUATION WITH POLYGONAL MESHES
Antonietti, P. F.
Da Veiga, L. Beirao
Scacchi, S.
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SIAM JOURNAL ON NUMERICAL ANALYSIS, 2016, 54 (01) : 34 - 56
[8] Uniformly Convergent C0-Nonconforming Triangular Prism Element for Fourth-Order Elliptic Singular Perturbation Problem
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Chen, Shaochun
Xiao, Liuchao
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2014, 30 (06) : 1785 - 1796
[9] A C1 Virtual Element Method on polyhedral meshes
da Veiga, L. Beirao
Dassi, F.
Russo, A.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 79 (07) : 1936 - 1955
[10] A C0 Nonconforming Virtual Element Method for the Kirchhoff Plate Obstacle Problem
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AXIOMS, 2024, 13 (05)

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