Convergence of Lagrange finite element methods for Maxwell eigenvalue problem in 3D

被引：1

作者：

Boffi, Daniele ^{[1
,2
]}

Gong, Sining ^{[3
]}

Guzman, Johnny ^{[3
]}

Neilan, Michael ^{[4
]}

机构：

[1] King Abdullah Univ Sci & Technol, Comp Elect & Math Sci & Engn Div, Thuwal 23955, Saudi Arabia

[2] Univ Pavia, I-27100 Pavia, Italy

[3] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[4] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2024年 / 44卷 / 04期

关键词：

Maxwell; eigenvalue; Worsey-Farin; APPROXIMATION; INTERPOLATION;

D O I：

10.1093/imanum/drad053

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove convergenceof the Maxwell eigenvalue problem using quadratic or higher Lagrange finite elements on Worsey-Farin splits in three dimensions. To do this, we construct two Fortin-like operators to prove uniform convergence of the corresponding source problem. We present numerical experiments to illustrate the theoretical results.

引用

页码：1911 / 1945

页数：35

共 37 条

[21] NEW MIXED ELEMENTS FOR MAXWELL EQUATIONS [J].

Duan, Huoyuan ;

Du, Zhijie ;

Liu, Wei ;

Zhang, Shangyou .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2019, 57 (01) :320-354

[22] A Note on the Shape Regularity of Worsey-Farin Splits [J].

Gong, Sining ;

Guzman, Johnny ;

Neilan, Michael .

JOURNAL OF SCIENTIFIC COMPUTING, 2023, 95 (02)

[23]

Grisvard P, 2011, CLASS APPL MATH, V69, P1, DOI 10.1137/1.9781611972030

[24] Exact sequences on Powell-Sabin splits [J].

Guzman, J. ;

Lischke, A. ;

Neilan, M. .

CALCOLO, 2020, 57 (02)

[25] EXACT SEQUENCES ON WORSEY-FARIN SPLITS [J].

Guzman, Johnny ;

Lischke, Anna ;

Neilan, Michael .

MATHEMATICS OF COMPUTATION, 2022, 91 (338) :2571-2608

[26] On the equivalence of fractional-order Sobolev semi-norms [J].

Heuer, Norbert .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 417 (02) :505-518

[27]

Hiptmair R, 2002, ACT NUMERIC, V11, P237

[28] Partially Discontinuous Nodal Finite Elements for H(curl) and H(div) [J].

Hu, Jun ;

Hu, Kaibo ;

Zhang, Qian .

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 2022, 22 (03) :613-629

[29] Spurious solutions for high-order curl problems [J].

Hu, Kaibo ;

Zhang, Qian ;

Han, Jiayu ;

Wang, Lixiu ;

Zhang, Zhimin .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2023, 43 (03) :1422-1449

[30]

Lai M.-J., 2007, Spline functions on triangulations, V110, DOI [10.1017/CBO9780511721588, DOI 10.1017/CBO9780511721588]

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