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

[1]

Alnaes M., 2015, Archive of numerical software 3.100, V3, DOI [10.11588/ans.2015.100.20553, DOI 10.11588/ANS.2015.100.20553]

[2]

Amrouche C, 1998, MATH METHOD APPL SCI, V21, P823, DOI 10.1002/(SICI)1099-1476(199806)21:9<823::AID-MMA976>3.0.CO

[3]

2-B

[4]

Arnold DN, 2006, ACT NUMERIC, V15, P1, DOI 10.1017/S0962492906210018

[5] A NODAL-BASED FINITE ELEMENT APPROXIMATION OF THE MAXWELL PROBLEM SUITABLE FOR SINGULAR SOLUTIONS [J].

Badia, Santiago ;

Codina, Ramon .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2012, 50 (02) :398-417

[6] Computational models of electromagnetic resonators: Analysis of edge element approximation [J].

Boffi, D ;

Fernandes, P ;

Gastaldi, L ;

Perugia, I .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, 36 (04) :1264-1290

[7] Approximation of eigenvalues in mixed form, Discrete Compactness Property, and application to hp mixed finite elements [J].

Boffi, Daniele .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (37-40) :3672-3681

[8] Convergence of Lagrange finite elements for the Maxwell eigenvalue problem in two dimensions [J].

Boffi, Daniele ;

Guzman, Johnny ;

Neilan, Michael .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2023, 43 (02) :663-691

[9]

Boffi D, 2010, ACTA NUMER, V19, P1, DOI 10.1017/S0962492910000012

[10] APPROXIMATION OF THE EIGENVALUE PROBLEM FOR THE TIME HARMONIC MAXWELL SYSTEM BY CONTINUOUS LAGRANGE FINITE ELEMENTS [J].

Bonito, Andrea ;

Guermond, Jean-Luc .

MATHEMATICS OF COMPUTATION, 2011, 80 (276) :1887-1910

← 1 2 3 4 →