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Residual based a posteriori error estimators for eddy current computation

ESAIM: M2AN, 34 1 (2000) 159-182
Published online: 2002-04-15

Adaptive multigrid and domain decomposition methods in the computation of electromagnetic fields

R.H.W. Hoppe
Journal of Computational and Applied Mathematics 168 (1-2) 245 (2004)
DOI: 10.1016/j.cam.2003.05.023

Improved Equilibrated Error Estimates for Open Boundary Magnetostatic Problems Based on Dual A and H Formulations

Yanpu Zhao and Zuqi Tang
IEEE Transactions on Magnetics 55 (6) 1 (2019)
DOI: 10.1109/TMAG.2019.2894058

Ap-hierarchical error estimator for a fe–be coupling formulation applied to electromagnetic scattering problems in ℝ3

F. Leydecker, M. Maischak, E.P. Stephan and M. Teltscher
Applicable Analysis 91 (2) 277 (2012)
DOI: 10.1080/00036811.2011.614605

Optimal control of Maxwell’s equations with regularized state constraints

Irwin Yousept
Computational Optimization and Applications 52 (2) 559 (2012)
DOI: 10.1007/s10589-011-9422-2

Contributions to Partial Differential Equations and Applications

Ricardo H. Nochetto and Benjamin Stamm
Computational Methods in Applied Sciences, Contributions to Partial Differential Equations and Applications 47 371 (2019)
DOI: 10.1007/978-3-319-78325-3_20

Convergence analysis of an adaptive edge element method for Maxwell's equations

Junqing Chen, Yifeng Xu and Jun Zou
Applied Numerical Mathematics 59 (12) 2950 (2009)
DOI: 10.1016/j.apnum.2009.07.003

Accuracy Verification Methods

Olli Mali, Pekka Neittaanmäki and Sergey Repin
Computational Methods in Applied Sciences, Accuracy Verification Methods 32 93 (2014)
DOI: 10.1007/978-94-007-7581-7_4

A New Heterogeneous Multiscale Method for Time-Harmonic Maxwell's Equations

Patrick Henning, Mario Ohlberger and Barbara Verfürth
SIAM Journal on Numerical Analysis 54 (6) 3493 (2016)
DOI: 10.1137/15M1039225

An Efficient Eddy Current Model for Nonlinear Maxwell Equations with Laminated Conductors

Xue Jiang and Weiying Zheng
SIAM Journal on Applied Mathematics 72 (4) 1021 (2012)
DOI: 10.1137/110857477

An adaptive inverse iteration for Maxwell eigenvalue problem based on edge elements

Junqing Chen, Yifeng Xu and Jun Zou
Journal of Computational Physics 229 (7) 2649 (2010)
DOI: 10.1016/j.jcp.2009.12.013

Edge Elements on Anisotropic Meshes and Approximation of the Maxwell Equations

Serge Nicaise
SIAM Journal on Numerical Analysis 39 (3) 784 (2001)
DOI: 10.1137/S003614290036988X

Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates

D. Harutyunyan, F. Izsák, J.J.W. van der Vegt and M.A. Botchev
Computer Methods in Applied Mechanics and Engineering 197 (17-18) 1620 (2008)
DOI: 10.1016/j.cma.2007.12.006

Unified framework for an a posteriori error analysis of non-standard finite element approximations of H(curl)-elliptic problems

C. Carstensen and R. H. W. Hoppe
Journal of Numerical Mathematics 17 (1) 27 (2009)
DOI: 10.1515/JNUM.2009.003

Edge element computations of eddy currents in laminated materials

Yueqiang Liu, A. Bondeson, R. Bergstrom, M.G. Larson and K. Samuelsson
IEEE Transactions on Magnetics 39 (3) 1758 (2003)
DOI: 10.1109/TMAG.2003.809843

Adaptive finite element frequency domain method for eddy current problems

Weiying Zheng and Feiran Zhang
Computer Methods in Applied Mechanics and Engineering 197 (13-16) 1233 (2008)
DOI: 10.1016/j.cma.2007.11.004

Homogenization of Quasi-static Maxwell's Equations

Xue Jiang and Weiying Zheng
Multiscale Modeling & Simulation 12 (1) 152 (2014)
DOI: 10.1137/130921398

Applied Mathematics in EM Studies with Special Emphasis on an Uncertainty Quantification and 3-D Integral Equation Modelling

Oleg Pankratov and Alexey Kuvshinov
Surveys in Geophysics 37 (1) 109 (2016)
DOI: 10.1007/s10712-015-9340-4

Adaptive hp-Finite Element Computations for Time-Harmonic Maxwell’s Equations

Xue Jiang, Linbo Zhang and Weiying Zheng
Communications in Computational Physics 13 (02) 559 (2013)
DOI: 10.4208/cicp.231111.090312a

A posteriori error estimation of goal-oriented quantities by the superconvergence patch recovery

S. Korotov, P. Neittaanmäki and S. Repin
Journal of Numerical Mathematics 11 (1) 33 (2003)
DOI: 10.1515/156939503322004882

Comparison of Residual and Hierarchical Finite Element Error Estimators in Eddy Current Problems

Patrick Dular, Zuqi Tang, Yvonnick Le Menach, Emmanuel Creuse and Francis Piriou
IEEE Transactions on Magnetics 50 (2) 501 (2014)
DOI: 10.1109/TMAG.2013.2285254

An explicit a posteriori error indicator for electromagnetic, finite element-boundary integral analysis

M.M. Botha and D.B. Davidson
IEEE Transactions on Antennas and Propagation 53 (11) 3717 (2005)
DOI: 10.1109/TAP.2005.858834

Adaptive Finite-Elemente-Simulation des Mehrfrequenz-Induktionshärtens in 3-D*

T. Petzold, D. Hömberg, D. Nadolski, A. Schulz and H. Stiele
HTM Journal of Heat Treatment and Materials 70 (1) 33 (2015)
DOI: 10.3139/105.110249

A FE/BE coupling for the 3D time-dependent eddy current problem. Part I: a priori error estimates

Ricardo A. Prato Torres, Ernst P. Stephan and Florian Leydecker
Computing 88 (3-4) 131 (2010)
DOI: 10.1007/s00607-010-0089-9

Residual-baseda posteriorierror estimation for the Maxwell’s eigenvalue problem

Daniele Boffi, Lucia Gastaldi, Rodolfo Rodríguez and Ivana Šebestová
IMA Journal of Numerical Analysis drw066 (2017)
DOI: 10.1093/imanum/drw066

The adaptive immersed interface finite element method for elliptic and Maxwell interface problems

Zhiming Chen, Yuanming Xiao and Linbo Zhang
Journal of Computational Physics 228 (14) 5000 (2009)
DOI: 10.1016/j.jcp.2009.03.044

Adaptive local multigrid methods for solving time-harmonic eddy-current problems

O. Sterz, A. Hauser and G. Wittum
IEEE Transactions on Magnetics 42 (2) 309 (2006)
DOI: 10.1109/TMAG.2005.859064

A residual-based a posteriori error estimator for the hp-finite element method for Maxwellʼs equations

M. Bürg
Applied Numerical Mathematics 62 (8) 922 (2012)
DOI: 10.1016/j.apnum.2012.02.007

Eddy-current computations using adaptive grids and edge elements

Yueqiang Liu, A. Bondeson, R. Bergstrom, et al.
IEEE Transactions on Magnetics 38 (2) 449 (2002)
DOI: 10.1109/20.996119

A posteriori error estimator for harmonic A‐φ formulation

Zuqi Tang, Andrzej Demenko, Yvonnick Le Menach, et al.
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 32 (4) 1219 (2013)
DOI: 10.1108/03321641311317040

Adaptive techniques for Landau–Lifshitz–Gilbert equation with magnetostriction

L’ubomír Baňas
Journal of Computational and Applied Mathematics 215 (2) 304 (2008)
DOI: 10.1016/j.cam.2006.03.043

Adaptive edge element approximation of H(curl)-elliptic optimal control problems with control constraints

Ronald H. W. Hoppe and Irwin Yousept
BIT Numerical Mathematics 55 (1) 255 (2015)
DOI: 10.1007/s10543-014-0497-x

Residual a Posteriori Estimator for Magnetoharmonic Potential Formulations With Global Quantities for the Source Terms

Zuqi Tang, Yvonnick Le Menach, Emmanuel Creuse, Serge Nicaise and Francis Piriou
IEEE Transactions on Magnetics 51 (3) 1 (2015)
DOI: 10.1109/TMAG.2014.2359770

Goal-oriented error estimation and h-adaptivity for Maxwell’s equations

P. Ingelström and A. Bondeson
Computer Methods in Applied Mechanics and Engineering 192 (22-24) 2597 (2003)
DOI: 10.1016/S0045-7825(03)00295-0

A Multiscale Approach and a Hybrid FE-FDTD Algorithm for 3D Time-Dependent Maxwell's Equations in Composite Materials

Liqun Cao, Keqi Li, Jianlan Luo and Yaushu Wong
Multiscale Modeling & Simulation 13 (4) 1446 (2015)
DOI: 10.1137/140999694

Numerical convergence and physical fidelity analysis for Maxwell’s equations in metamaterials

Jichun Li
Computer Methods in Applied Mechanics and Engineering 198 (37-40) 3161 (2009)
DOI: 10.1016/j.cma.2009.05.018

On Zienkiewicz–Zhu error estimators for Maxwell's equations

Serge Nicaise
Comptes Rendus Mathematique 340 (9) 697 (2005)
DOI: 10.1016/j.crma.2005.03.016

Robust a posteriori error estimation for the Maxwell equations

Sarah Cochez-Dhondt and Serge Nicaise
Computer Methods in Applied Mechanics and Engineering 196 (25-28) 2583 (2007)
DOI: 10.1016/j.cma.2006.11.025

Multiscale Asymptotic Method for Maxwell's Equations in Composite Materials

Liqun Cao, Ya Zhang, Walter Allegretto and Yanping Lin
SIAM Journal on Numerical Analysis 47 (6) 4257 (2010)
DOI: 10.1137/080741276

A Posteriori Error Estimation and Adaptive Mesh Refinement Controlling in Finite Element Analysis of 3-D Steady State Eddy Current Fields

Jinbiao Li, Dexin Xie and Xiaoming Liu
IEEE Transactions on Magnetics 46 (8) 3500 (2010)
DOI: 10.1109/TMAG.2010.2045486

A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling

Zhengyong Ren, Thomas Kalscheuer, Stewart Greenhalgh and Hansruedi Maurer
Geophysical Journal International 194 (2) 700 (2013)
DOI: 10.1093/gji/ggt154

Robust and scalable 3-D geo-electromagnetic modelling approach using the finite element method

Alexander V. Grayver and Markus Bürg
Geophysical Journal International 198 (1) 110 (2014)
DOI: 10.1093/gji/ggu119

Helmholtz decomposition of vector fields with mixed boundary conditions and an application to a posteriori finite element error analysis of the Maxwell system

Emmanuel Creusé, Serge Nicaise and Zuqi Tang
Mathematical Methods in the Applied Sciences 38 (4) 738 (2015)
DOI: 10.1002/mma.3104

A Posteriori Error Estimates for Finite Element Exterior Calculus: The de Rham Complex

Alan Demlow and Anil N. Hirani
Foundations of Computational Mathematics 14 (6) 1337 (2014)
DOI: 10.1007/s10208-014-9203-2

Finite Element Analysis of an Optimal Control Problem in the Coefficients of Time-Harmonic Eddy Current Equations

Irwin Yousept
Journal of Optimization Theory and Applications 154 (3) 879 (2012)
DOI: 10.1007/s10957-012-0040-7

Interior Penalty Discontinuous Galerkin Method for Maxwell’s Equations in Cold Plasma

Yunqing Huang and Jichun Li
Journal of Scientific Computing 41 (3) 321 (2009)
DOI: 10.1007/s10915-009-9300-6

Mathematics — Key Technology for the Future

Ronald H. W. Hoppe, Peter Böhm, George Mazurkevitch, et al.
Mathematics — Key Technology for the Future 365 (2003)
DOI: 10.1007/978-3-642-55753-8_30

Residual Based a Posteriori Error Estimators for Harmonic ${\bf A}/\varphi$ and ${\bf T}/\Omega$ Formulations in Eddy Current Problems

Zuqi Tang, Yvonnick Le Menach, Emmanuel Creuse, et al.
IEEE Transactions on Magnetics 49 (5) 1721 (2013)
DOI: 10.1109/TMAG.2013.2241408

Residual and equilibrated error estimators for magnetostatic problems solved by finite element method

Zuqi Tang, Yvonnick Le Menach, Emmanuel Creuse, et al.
IEEE Transactions on Magnetics 49 (12) 5715 (2013)
DOI: 10.1109/TMAG.2013.2271993

Space-Time Residual-Based a posteriori Estimator for the $A-\varphi$ Formulation in Eddy Current Problems

Roberta Tittarelli, Yvonnick Le Menach, Emmanuel Creuse, et al.
IEEE Transactions on Magnetics 51 (3) 1 (2015)
DOI: 10.1109/TMAG.2014.2354357

Convergence of an automatic hp-adaptive finite element strategy for Maxwellʼs equations

M. Bürg
Applied Numerical Mathematics 72 188 (2013)
DOI: 10.1016/j.apnum.2013.04.008

Modeling and analysis of the optical black hole in metamaterials by the finite element time-domain method

Wei Yang, Jichun Li and Yunqing Huang
Computer Methods in Applied Mechanics and Engineering 304 501 (2016)
DOI: 10.1016/j.cma.2016.02.029

Mathematical analysis and finite element simulation of a magnetized ferrite model

Jichun Li, Yunqing Huang and Wei Yang
Journal of Computational and Applied Mathematics 292 279 (2016)
DOI: 10.1016/j.cam.2015.07.002

An H - ψ formulation for the three-dimensional eddy current problem in laminated structures

Peijun Li and Weiying Zheng
Journal of Differential Equations 254 (8) 3476 (2013)
DOI: 10.1016/j.jde.2013.01.028

Uniform convergence of local multigrid methods for the time-harmonic Maxwell equation

Huangxin Chen, Ronald H.W. Hoppe and Xuejun Xu
ESAIM: Mathematical Modelling and Numerical Analysis 47 (1) 125 (2013)
DOI: 10.1051/m2an/2012023

An Adaptive FEM Based on Magnetic Field Conservation Applying to Ferromagnetic Problems

So Noguchi, Shinya Matsutomo and Vlatko Cingoski
IEEE Transactions on Magnetics 54 (3) 1 (2018)
DOI: 10.1109/TMAG.2017.2754862

Comparison of Numerical Error Estimators for Eddy-Current Problems Solved by FEM

R. Tittarelli, Y. Le Menach, F. Piriou, et al.
IEEE Transactions on Magnetics 54 (3) 1 (2018)
DOI: 10.1109/TMAG.2017.2736601

A priori and computable a posteriori error estimates for an HDG method for the coercive Maxwell equations

Huangxin Chen, Weifeng Qiu and Ke Shi
Computer Methods in Applied Mechanics and Engineering 333 287 (2018)
DOI: 10.1016/j.cma.2018.01.030

RESIDUAL-BASED A POSTERIORI ESTIMATORS FOR THE A - φ MAGNETODYNAMIC HARMONIC FORMULATION OF THE MAXWELL SYSTEM

EMMANUEL CREUSÉ, SERGE NICAISE, ZUQI TANG, et al.
Mathematical Models and Methods in Applied Sciences 22 (05) 1150028 (2012)
DOI: 10.1142/S021820251150028X

A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics

Timon Rabczuk, Stéphane Bordas and Goangseup Zi
Computational Mechanics 40 (3) 473 (2007)
DOI: 10.1007/s00466-006-0122-1

An Adaptive P 1 Finite Element Method for Two-Dimensional Maxwell’s Equations

S. C. Brenner, J. Gedicke and L.-Y. Sung
Journal of Scientific Computing 55 (3) 738 (2013)
DOI: 10.1007/s10915-012-9658-8

An Adaptive Finite Element Method for the H- ψ Formulation of Time-dependent Eddy Current Problems

Weiying Zheng, Zhiming Chen and Long Wang
Numerische Mathematik 103 (4) 667 (2006)
DOI: 10.1007/s00211-006-0008-3

An adaptive edge element method and its convergence for a Saddle-Point problem from magnetostatics

Junqing Chen, Yifeng Xu and Jun Zou
Numerical Methods for Partial Differential Equations 28 (5) 1643 (2012)
DOI: 10.1002/num.20697

Functional approach to a posteriori error estimation for elliptic optimal control problems with distributed control

A. Gaevskaya, R. H. W. Hoppe and S. Repin
Journal of Mathematical Sciences 144 (6) 4535 (2007)
DOI: 10.1007/s10958-007-0293-0

Unified Analysis of Leap-Frog Methods for Solving Time-Domain Maxwell’s Equations in Dispersive Media

Jichun Li
Journal of Scientific Computing 47 (1) 1 (2011)
DOI: 10.1007/s10915-010-9417-7

Numerical Study of the Plasma-Lorentz Model in Metamaterials

Jichun Li, Yunqing Huang and Wei Yang
Journal of Scientific Computing 54 (1) 121 (2013)
DOI: 10.1007/s10915-012-9608-5

Error-driven dynamical hp-meshes with the Discontinuous Galerkin Method for three-dimensional wave propagation problems

Sascha M. Schnepp
Journal of Computational and Applied Mathematics 270 353 (2014)
DOI: 10.1016/j.cam.2013.12.038

Efficient solvers for nonlinear time-periodic eddy current problems

Florian Bachinger, Ulrich Langer and Joachim Schöberl
Computing and Visualization in Science 9 (4) 197 (2006)
DOI: 10.1007/s00791-006-0023-z

Adaptive FE-BE coupling for an electromagnetic problem in ℝ3-A residual error estimator

Florian Leydecker, Matthias Maischak, Ernst P. Stephan and Matthias Teltscher
Mathematical Methods in the Applied Sciences 33 (18) 2162 (2010)
DOI: 10.1002/mma.1389

Singularities of eddy current problems

Martin Costabel, Monique Dauge and Serge Nicaise
ESAIM: Mathematical Modelling and Numerical Analysis 37 (5) 807 (2003)
DOI: 10.1051/m2an:2003056

Developing Finite Element Methods for Maxwell's Equations in a Cole–Cole Dispersive Medium

Jichun Li, Yunqing Huang and Yanping Lin
SIAM Journal on Scientific Computing 33 (6) 3153 (2011)
DOI: 10.1137/110827624

Automated Goal-Oriented Error Control I: Stationary Variational Problems

Marie E. Rognes and Anders Logg
SIAM Journal on Scientific Computing 35 (3) C173 (2013)
DOI: 10.1137/10081962X

Finite element study of the Lorentz model in metamaterials

Jichun Li
Computer Methods in Applied Mechanics and Engineering 200 (5-8) 626 (2011)
DOI: 10.1016/j.cma.2010.09.008

An adaptive anisotropic perfectly matched layer method for 3-D time harmonic electromagnetic scattering problems

Zhiming Chen, Tao Cui and Linbo Zhang
Numerische Mathematik 125 (4) 639 (2013)
DOI: 10.1007/s00211-013-0550-8

Convergence analysis of an adaptive edge finite element method for the 2D eddy current equations

C. Carstensen and R. H. W. Hoppe
Journal of Numerical Mathematics 13 (1) 19 (2005)
DOI: 10.1515/1569395054069017

A posteriori error estimates for fem–bem couplings of three-dimensional electromagnetic problems

E.P. Stephan and M. Maischak
Computer Methods in Applied Mechanics and Engineering 194 (2-5) 441 (2005)
DOI: 10.1016/j.cma.2004.03.017

A priori and posteriori error analysis for time-dependent Maxwell’s equations

Jichun Li and Yanping Lin
Computer Methods in Applied Mechanics and Engineering 292 54 (2015)
DOI: 10.1016/j.cma.2014.08.009

Numerical Mathematics and Advanced Applications

R. H. W. Hoppe
Numerical Mathematics and Advanced Applications 201 (2003)
DOI: 10.1007/978-88-470-2089-4_19

NPBS-based adaptive finite element method for static electromagnetic problems

Fan Wang, Yufeng Nie, Weiwei Zhang and Wei Guo
Journal of Electromagnetic Waves and Applications 30 (15) 2020 (2016)
DOI: 10.1080/09205071.2016.1237896

Time-domain finite element method and analysis for modeling of surface plasmon polaritons

Wei Yang, Jichun Li and Yunqing Huang
Computer Methods in Applied Mechanics and Engineering 372 113349 (2020)
DOI: 10.1016/j.cma.2020.113349

Residual-based a posteriori error estimates for a nonconforming finite element discretization of the Stokes–Darcy coupled problem: isotropic discretization

Serge Nicaise, Bernardin Ahounou and Wilfrid Houedanou
Afrika Matematika 27 (3-4) 701 (2016)
DOI: 10.1007/s13370-015-0370-3

An Adaptive FEM for a Maxwell Interface Problem

Huoyuan Duan, Fengjuan Qiu, Roger C. E. Tan and Weiying Zheng
Journal of Scientific Computing 67 (2) 669 (2016)
DOI: 10.1007/s10915-015-0098-0

Developing a Time-Domain Finite Element Method for the Lorentz Metamaterial Model and Applications

Wei Yang, Yunqing Huang and Jichun Li
Journal of Scientific Computing 68 (2) 438 (2016)
DOI: 10.1007/s10915-015-0144-y

A Priori and a Posteriori Error Estimates for H(div)-Elliptic Problem with Interior Penalty Method

Yuping Zeng and Jinru Chen
Communications in Computational Physics 14 (3) 753 (2013)
DOI: 10.4208/cicp.040412.071112a

Residual-based a posteriori estimators for the potential formulations of electrostatic and time-harmonic eddy current problems with voltage or current excitation

Chao Chen, Emmanuel Creusé, Serge Nicaise and Zuqi Tang
International Journal for Numerical Methods in Engineering 107 (5) 377 (2016)
DOI: 10.1002/nme.5168

A multiscale approach and a hybrid FE-BE algorithm for heterogeneous scattering of Maxwell’s equations

Yongwei Zhang, Liqun Cao, Yangde Feng and Wu Wang
Journal of Computational and Applied Mathematics (2017)
DOI: 10.1016/j.cam.2017.01.017

Simulation of multi-frequency-induction-hardening including phase transitions and mechanical effects

Dietmar Hömberg, Qingzhe Liu, Jonathan Montalvo-Urquizo, et al.
Finite Elements in Analysis and Design 121 86 (2016)
DOI: 10.1016/j.finel.2016.07.012

A New Adaptive Mesh Refinement Method in FEA Based on Magnetic Field Conservation at Elements Interfaces and Non-Conforming Mesh Refinement Technique

So Noguchi, Takuto Naoe, Hajime Igarashi, et al.
IEEE Transactions on Magnetics 53 (6) 1 (2017)
DOI: 10.1109/TMAG.2017.2655049

A posterioriresidual error estimators with mixed boundary conditions for quasi-static electromagnetic problems

Zuqi Tang, Andrzej Demenko, Ivo Doležel, Kay Hameyer,, Yvonnick Le-menach, et al.
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 34 (3) 724 (2015)
DOI: 10.1108/COMPEL-10-2014-0256

A Unified Variational Formulation for the Parabolic-Elliptic Eddy Current Equations

Lilian Arnold and Bastian Harrach
SIAM Journal on Applied Mathematics 72 (2) 558 (2012)
DOI: 10.1137/110831477

An Iterative Substructuring Algorithm for Two-Dimensional Problems in H(curl)

Clark R. Dohrmann and Olof B. Widlund
SIAM Journal on Numerical Analysis 50 (3) 1004 (2012)
DOI: 10.1137/100818145

Optimal Control of Quasilinear $\boldsymbol{H}(\mathbf{curl})$-Elliptic Partial Differential Equations in Magnetostatic Field Problems

Irwin Yousept
SIAM Journal on Control and Optimization 51 (5) 3624 (2013)
DOI: 10.1137/120904299

Eddy Current Model for Nondestructive Evaluation with Thin Cracks

Xue Jiang, Peijun Li and Weiying Zheng
SIAM Journal on Scientific Computing 38 (2) A973 (2016)
DOI: 10.1137/15M1015492

An Adaptive Finite Element Method for the Eddy Current Model with Circuit/Field Couplings

Junqing Chen, Zhiming Chen, Tao Cui and Lin-Bo Zhang
SIAM Journal on Scientific Computing 32 (2) 1020 (2010)
DOI: 10.1137/080713112

An Adaptive Multilevel Method for Time‐Harmonic Maxwell Equations with Singularities

Zhiming Chen, Long Wang and Weiying Zheng
SIAM Journal on Scientific Computing 29 (1) 118 (2007)
DOI: 10.1137/050636012

Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\mathrm{curl}}$-Conforming High Order Finite Element Methods

Bärbel Janssen and Guido Kanschat
SIAM Journal on Scientific Computing 33 (4) 2095 (2011)
DOI: 10.1137/090778523

A recovery-based a posteriori error estimator for (curl) interface problems

Zhiqiang Cai and Shuhao Cao
Computer Methods in Applied Mechanics and Engineering 296 169 (2015)
DOI: 10.1016/j.cma.2015.08.002

A Dynamic $p$ -Adaptive DGTD Algorithm for Electromagnetic and Multiphysics Simulations

Su Yan and Jian-Ming Jin
IEEE Transactions on Antennas and Propagation 65 (5) 2446 (2017)
DOI: 10.1109/TAP.2017.2676724

A Posteriori Error Estimates for Maxwell’s Eigenvalue Problem

Daniele Boffi, Lucia Gastaldi, Rodolfo Rodríguez and Ivana Šebestová
Journal of Scientific Computing 78 (2) 1250 (2019)
DOI: 10.1007/s10915-018-0808-5

Numerical analysis of a finite element method for the electromagnetic concentrator model

Yunqing Huang and Jichun Li
Advances in Computational Mathematics 46 (6) (2020)
DOI: 10.1007/s10444-020-09817-8

The Impact of Applications on Mathematics

Dietmar Hömberg, Thomas Petzold and Elisabetta Rocca
Mathematics for Industry, The Impact of Applications on Mathematics 1 257 (2014)
DOI: 10.1007/978-4-431-54907-9_19

Functional a posteriori estimates for Maxwell’s equation

S. Repin
Journal of Mathematical Sciences 142 (1) 1821 (2007)
DOI: 10.1007/s10958-007-0091-8

Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials

Jichun Li and Yunqing Huang
Springer Series in Computational Mathematics, Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials 43 215 (2013)
DOI: 10.1007/978-3-642-33789-5_8

Convergence of adaptive edge finite element methods forH(curl)-elliptic problems

Liuqiang Zhong, Shi Shu, Long Chen and Jinchao Xu
Numerical Linear Algebra with Applications n/a (2010)
DOI: 10.1002/nla.694

Adaptive Finite Element Method for the Maxwell Eigenvalue Problem

Daniele Boffi and Lucia Gastaldi
SIAM Journal on Numerical Analysis 57 (1) 478 (2019)
DOI: 10.1137/18M1179389

A FE/BE coupling for the 3D time-dependent eddy current problem. Part II: a posteriori error estimates and adaptive computations

Ricardo A. Prato Torres, Ernst P. Stephan and Florian Leydecker
Computing 88 (3-4) 155 (2010)
DOI: 10.1007/s00607-010-0091-2

Multiscale, Nonlinear and Adaptive Approximation

Ricardo H. Nochetto, Kunibert G. Siebert and Andreas Veeser
Multiscale, Nonlinear and Adaptive Approximation 409 (2009)
DOI: 10.1007/978-3-642-03413-8_12

Applied and Numerical Partial Differential Equations

Pekka Neittaanmäki and Sergey Repin
Computational Methods in Applied Sciences, Applied and Numerical Partial Differential Equations 15 199 (2010)
DOI: 10.1007/978-90-481-3239-3_15

Robust a posteriori error estimation for finite element approximation to (curl) problem

Zhiqiang Cai, Shuhao Cao and Rob Falgout
Computer Methods in Applied Mechanics and Engineering 309 182 (2016)
DOI: 10.1016/j.cma.2016.06.007

An Advanced EM-Plasma Simulator Based on the DGTD Algorithm With Dynamic Adaptation and Multirate Time Integration Techniques

Su Yan, Jiwei Qian and Jian-Ming Jin
IEEE Journal on Multiscale and Multiphysics Computational Techniques 4 76 (2019)
DOI: 10.1109/JMMCT.2019.2901533

Optimal Control of Complex Structures

Ronald H. W. Hoppe, Svetozara Petrova and Volker Schulz
Optimal Control of Complex Structures 119 (2001)
DOI: 10.1007/978-3-0348-8148-7_10

Two guaranteed equilibrated error estimators for Harmonic formulations in eddy current problems

E. Creusé, Y. Le Menach, S. Nicaise, F. Piriou and R. Tittarelli
Computers & Mathematics with Applications 77 (6) 1549 (2019)
DOI: 10.1016/j.camwa.2018.08.046

On the Magneto-Heat Coupling Model for Large Power Transformers

Xujing Li, Shipeng Mao, Kangkang Yang and Weiying Zheng
Communications in Computational Physics 22 (3) 683 (2017)
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DOI: 10.1007/978-3-642-33789-5_4

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DOI: 10.1007/978-3-642-33789-5_3

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DOI: 10.1007/978-3-642-33789-5_7

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DOI: 10.1007/978-3-642-33789-5_9

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DOI: 10.1007/978-3-642-33789-5_6

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DOI: 10.1007/978-3-642-33789-5_2

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DOI: 10.1007/978-3-642-33789-5_5

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DOI: 10.1002/jnm.2626

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Journal of Computational and Applied Mathematics 376 112860 (2020)
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DOI: 10.1016/j.camwa.2020.02.001

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SIAM Journal on Numerical Analysis 58 (3) 1941 (2020)
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