Encyclopedia of Applied and Computational Mathematics

2015 Edition
| Editors: Björn Engquist

Electromagnetics-Maxwell Equations

  • Leszek F. Demkowicz
Reference work entry
First Online:
DOI: https://doi.org/10.1007/978-3-540-70529-1_511
How to cite

Mathematics Subject Classification

65N30; 35L15

Synonyms

H(curl)-conforming elements; Edge elements

Short Definition

Finite element method is a discretization method for Maxwell equations. Developed originally for elliptic problems, finite elements must deal with a different energy setting and linear dependence of Maxwell equations.

Description

Maxwell Equations

Maxwell equations (Heaviside’s formulation) include equations of Ampère(with Maxwell’s correction) and Faraday, Gauss’ electric and magnetic laws, and conservation of charge equation. In this entry we restrict ourselves to the time-harmonic version of the Maxwell equations which can be obtained by Fourier transforming the transient Maxwell equations or, equivalently, using e j ω t ansatz in time.
$$\displaystyle\begin{array}{rcl} \left \{\begin{array}{@{}l@{\quad }l@{}} \nabla \times E = -j\omega (\mu H) \quad \\ \qquad \qquad \qquad \text{Faraday law} \quad \\ \nabla \times H = J^{\mathrm{imp}} +\sigma E + j\omega (\epsilon...
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Leszek F. Demkowicz
    • 1
  1. 1.Institute for Computational Engineering and Sciences (ICES)The University of Texas at AustinAustinUSA