Nonconforming finite element approximation of time-dependent Maxwell's equations in Debye medium

2014 ◽  
Vol 30 (5) ◽  
pp. 1654-1673 ◽  
Author(s):  
Dongyang Shi ◽  
Changhui Yao
Keyword(s):  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Finite Element Approximation ◽  
Time Dependent ◽  
Element Approximation ◽  
Nonconforming Finite Element

Superconvergent recovery of edge finite element approximation for Maxwell’s equations

2020 ◽  
Vol 371 ◽  
pp. 113302 ◽  
Author(s):  
Chao Wu ◽  
Yunqing Huang ◽  
Nianyu Yi ◽  
Jinyun Yuan
Keyword(s):  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Finite Element Approximation ◽  
Element Approximation

scholarly journals Finite Element Approximation of Maxwell's Equations with Debye Memory

2010 ◽  
Vol 2010 ◽  
pp. 1-28 ◽  
Author(s):  
Simon Shaw
Keyword(s):  
Finite Element ◽  
Electric Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Mixed Finite Element ◽  
Finite Element Approximation ◽  
Constitutive Law ◽  
Fading Memory ◽  
Element Approximation ◽  
Long Time

Maxwell's equations in a bounded Debye medium are formulated in terms of the standard partial differential equations of electromagnetism with a Volterra-type history dependence of the polarization on the electric field intensity. This leads to Maxwell's equations with memory. We make a correspondence between this type of constitutive law and the hereditary integral constitutive laws from linear viscoelasticity, and we are then able to apply known results from viscoelasticity theory to this Maxwell system. In particular, we can show long-time stability by shunning Gronwall's lemma and estimating the history kernels more carefully by appeal to the underlying physical fading memory. We also give a fully discrete scheme for the electric field wave equation and derive stability bounds which are exactly analogous to those for the continuous problem, thus providing a foundation for long-time numerical integration. We finish by also providing error bounds for which the constant grows, at worst, linearly in time (excluding the time dependence in the norms of the exact solution). Although the first (mixed) finite element error analysis for the Debye problem was given by Li (2007), this seems to be the first time sharp constants have been given for this problem.

Well‐posedness and finite element approximation of time dependent generalized bioconvective flow

2019 ◽  
Vol 36 (4) ◽  
pp. 709-733
Author(s):  
Yanzhao Cao ◽  
Song Chen ◽  
Hans‐Werner Wyk
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Time Dependent ◽  
Element Approximation ◽  
Well Posedness ◽  
Bioconvective Flow
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