%0 Generic %1 monk2019finite %A Monk, Peter %A Zhang, Yangwen %D 2019 %K 35q60-pdes-in-connection-with-optics-and-electromagnetic-theory 65n30-pdes-bvps-finite-elements 65z05-applications-of-numerical-analysis-to-physics 78-01-optics-electromagnetic-theory-instructional-exposition 78a25-electromagnetic-theory-general 78a45-diffraction-scattering 78a46-inverse-problems-in-optics-and-electromagnetic-theory 78m10-optics-electromagnetism-finite-element-method %T Finite Element Methods for Maxwell's Equations %U http://arxiv.org/abs/1910.10069 %X We survey finite element methods for approximating the time harmonic Maxwell equations. We concentrate on comparing error estimates for problems with spatially varying coefficients. For the conforming edge finite element methods, such estimates allow, at least, piecewise smooth coefficients. But for Discontinuous Galerkin (DG) methods, the state of the art of error analysis is less advanced (we consider three DG families of methods: Interior Penalty type, Hybridizable DG, and Trefftz type methods). Nevertheless, DG methods offer significant potential advantages compared to conforming methods.

@misc{monk2019finite, abstract = {We survey finite element methods for approximating the time harmonic Maxwell equations. We concentrate on comparing error estimates for problems with spatially varying coefficients. For the conforming edge finite element methods, such estimates allow, at least, piecewise smooth coefficients. But for Discontinuous Galerkin (DG) methods, the state of the art of error analysis is less advanced (we consider three DG families of methods: Interior Penalty type, Hybridizable DG, and Trefftz type methods). Nevertheless, DG methods offer significant potential advantages compared to conforming methods.}, added-at = {2022-02-17T06:41:10.000+0100}, author = {Monk, Peter and Zhang, Yangwen}, biburl = {https://www.bibsonomy.org/bibtex/2eb84670ed3164818b4c3aa10075e1e08/gdmcbain}, description = {Finite Element Methods for Maxwell's Equations}, interhash = {4e641ddbf8443a76dbe9767cd98884f0}, intrahash = {eb84670ed3164818b4c3aa10075e1e08}, keywords = {35q60-pdes-in-connection-with-optics-and-electromagnetic-theory 65n30-pdes-bvps-finite-elements 65z05-applications-of-numerical-analysis-to-physics 78-01-optics-electromagnetic-theory-instructional-exposition 78a25-electromagnetic-theory-general 78a45-diffraction-scattering 78a46-inverse-problems-in-optics-and-electromagnetic-theory 78m10-optics-electromagnetism-finite-element-method}, note = {cite arxiv:1910.10069}, timestamp = {2022-02-17T06:41:10.000+0100}, title = {Finite Element Methods for Maxwell's Equations}, url = {http://arxiv.org/abs/1910.10069}, year = 2019 }