Finite element approximation of electromagnetic fields using non-fitting meshes for Geophysics - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles SIAM Journal on Numerical Analysis Year : 2018

Finite element approximation of electromagnetic fields using non-fitting meshes for Geophysics

Abstract

We analyze the use of non-fitting meshes for simulating the propagation of electromagnetic waves inside the Earth. In order to take into account subcell conductivity variations, we propose a simple " exact integration technique " that avoids the use of parameter homogenization and employs standard edge finite element basis functions. For our geophysical applications, we consider a 3D Maxwell's system with piecewise constant conductivity and globally constant permittivity and permeability. The model is analysed and discretized using both the E and H-formulations. Our main contribution is to develop a sharp error estimate for both the electric and magnetic fields. In the presence of singularities, our estimate shows that the magnetic field approximation is converging faster than the electric field approximation. As a result, we conclude that error estimates available in the literature for Nédélec's elements with fitting meshes are sharp with respect to the electric field error, but provide pessimistic convergence rates for the magnetic field in our geophysical applications. Another surprising consequence of our analysis is that non-fitting meshes deliver the same convergence rate than fitting meshes to approximate the magnetic field. Our theoretical results are numerically illustrated via 2D experiments. For the analyzed cases, the accuracy loss due to the use of non-fitting meshes is limited, even for high conductivity contrasts.
Fichier principal
Vignette du fichier
paper_maxwell.pdf (573.7 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01706452 , version 1 (11-02-2018)
hal-01706452 , version 2 (16-12-2018)

Identifiers

  • HAL Id : hal-01706452 , version 1

Cite

Théophile Chaumont-Frelet, Serge Nicaise, David Pardo. Finite element approximation of electromagnetic fields using non-fitting meshes for Geophysics. SIAM Journal on Numerical Analysis, In press. ⟨hal-01706452v1⟩
216 View
824 Download

Share

Gmail Facebook X LinkedIn More