A NONCONFORMING PENALTY METHOD FOR A TWO-DIMENSIONAL CURL-CURL PROBLEM

被引：9
|
作者：
Brenner, Susanne C. [1 ,2 ]
Li, Fengyan [3 ]
Sung, Li-Yeng [2 ]
机构：
[1] Louisiana State Univ, Ctr Computat & Technol, Baton Rouge, LA 70803 USA
[2] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
[3] Rensselaer Polytech Inst, Dept Math Sci, Troy, NY 12180 USA
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2009年 / 19卷 / 04期
基金：
美国国家科学基金会;
关键词：
Curl-curl problem; Maxwell equations; Maxwell eigenvalues; nonconforming finite element method; DISCONTINUOUS GALERKIN APPROXIMATION; HARMONIC MAXWELL EQUATIONS; MIXED FINITE-ELEMENTS; WEIGHTED REGULARIZATION; POLYHEDRAL DOMAINS; OPERATOR; CONVERGENCE;
D O I：
10.1142/S0218202509003565
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A nonconforming finite element method for a two-dimensional curl-curl problem is studied in this paper. It uses weakly continuous P(1) vector fields and penalizes the local divergence. Two consistency terms involving the jumps of the vector fields across element boundaries are also included to ensure the convergence of the scheme. Optimal convergence rates ( up to an arbitrary positive epsilon) in both the energy norm and the L(2) norm are established on graded meshes. This scheme can also be used in the computation of Maxwell eigenvalues without generating spurious eigenmodes. The theoretical results are confirmed by numerical experiments.
引用
收藏
页码：651 / 668
页数：18
相关论文
共 50 条
  • [21] Reducing the curl-curl matrix bandwidth in 2D magnetostatics using tree-cotree method
    Domnikov, Petr
    2019 INTERNATIONAL SYMPOSIUM ON ADVANCED ELECTRICAL AND COMMUNICATION TECHNOLOGIES (ISAECT), 2019,
  • [22] Superconvergence of a Nonconforming Brick Element for the Quad-Curl Problem
    Zhou, Xinchen
    Meng, Zhaoliang
    Niu, Hexin
    INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2024, 21 (06)
  • [23] An algebraic multigrid method for high order time-discretizations of the div-grad and the curl-curl equations
    Boonen, Tim
    Van lent, Jan
    Vandewalle, Stefan
    APPLIED NUMERICAL MATHEMATICS, 2009, 59 (3-4) : 507 - 521
  • [24] A New Family of Nonconforming Elements with H(curl)-Continuity for the 3D Quad-Curl Problem
    Zhang, Baiju
    Zhang, Zhimin
    COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2023, 33 (04) : 1069 - 1089
  • [25] AN ITERATIVE SUBSTRUCTURING ALGORITHM FOR TWO-DIMENSIONAL PROBLEMS IN H(CURL)
    Dohrmann, Clark R.
    Widlund, Olof B.
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2012, 50 (03) : 1004 - 1028
  • [26] Gradient recovery based finite element methods for the two-dimensional quad-curl problem
    Fang, Yuzhi
    Feng, Yuan
    Xu, Minqiang
    Zhang, Lei
    APPLIED MATHEMATICS LETTERS, 2023, 146
  • [27] POLYNOMIAL PRESERVING RECOVERY AND A POSTERIORI ERROR ESTIMATES FOR THE TWO-DIMENSIONAL QUAD-CURL PROBLEM
    Zhang, Baiju
    Zhang, Zhimin
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2023, 28 (02): : 1323 - 1341
  • [28] POLYNOMIAL PRESERVING RECOVERY AND A POSTERIORI ERROR ESTIMATES FOR THE TWO-DIMENSIONAL QUAD-CURL PROBLEM
    Zhang, Baiju
    Zhang, Zhimin
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2022,
  • [29] Non-nested geometric multigrid method using consistency error correction for discrete magnetic curl-curl formulations
    Clemens, M
    Feigh, S
    Wilke, M
    Weiland, T
    COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING, 2004, 23 (04) : 913 - 922
  • [30] Method for Analytically Finding the Left and Right Nullspace of Curl-Curl Operator in Unsymmetrical Finite-Difference Subgridding Algorithm
    Liu, Hongyang
    Jiao, Dan
    2024 INTERNATIONAL APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY SYMPOSIUM, ACES 2024, 2024,
12345