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

DOI10.1051/m2an/2012023zbMath1278.65167OpenAlexW2023052299MaRDI QIDQ2836458

Xuejun Xu, Huangxin Chen, Ronald H. W. Hoppe

Publication date: 3 July 2013

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/m2an/2012023

zbMATH Keywords

convergencenumerical examplesadaptive mesh refinementoptimalityMaxwell equationsmultigrid methodsa posteriori error estimatorsindefiniteNédélec edge elementsadaptive edge finite element methodslocal Hiptmair smoothersmultilevel iterative schemes

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Electromagnetic theory (general) (78A25) Maxwell equations (35Q61)

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A Robust Multilevel Method for the Time-harmonic Maxwell Equation with High Wave Number ⋮ Extension by zero in discrete trace spaces: Inverse estimates ⋮ Multilevel decompositions and norms for negative order Sobolev spaces

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