Version 1
: Received: 29 January 2024 / Approved: 30 January 2024 / Online: 30 January 2024 (14:16:10 CET)
How to cite:
Beilina, L.; Ruas, V. Explicit P1 Finite Element Solution of the Maxwell-Wave Equation Coupling Problem with Absorbing b. c.. Preprints2024, 2024012097. https://doi.org/10.20944/preprints202401.2097.v1
Beilina, L.; Ruas, V. Explicit P1 Finite Element Solution of the Maxwell-Wave Equation Coupling Problem with Absorbing b. c.. Preprints 2024, 2024012097. https://doi.org/10.20944/preprints202401.2097.v1
Beilina, L.; Ruas, V. Explicit P1 Finite Element Solution of the Maxwell-Wave Equation Coupling Problem with Absorbing b. c.. Preprints2024, 2024012097. https://doi.org/10.20944/preprints202401.2097.v1
APA Style
Beilina, L., & Ruas, V. (2024). Explicit <em>P1</em> Finite Element Solution of the Maxwell-Wave Equation Coupling Problem with Absorbing b. c.. Preprints. https://doi.org/10.20944/preprints202401.2097.v1
Chicago/Turabian Style
Beilina, L. and Vitoriano Ruas. 2024 "Explicit <em>P1</em> Finite Element Solution of the Maxwell-Wave Equation Coupling Problem with Absorbing b. c." Preprints. https://doi.org/10.20944/preprints202401.2097.v1
Abstract
In this paper we address the approximation of the coupling problem for the wave equation and Maxwell's equations of electromagnetism in the time domain in terms of the electric field, by means of a nodal linear finite-element discretization in space, combined with a classical'explicit finite-difference scheme for the time discretization. Our study applies to the particular case where the dielectric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this sub-domain Maxwell's equations hold. Outside this sub-domain the wave equation holds, which may correspond to the Maxwell's equations with a constant permittivity under certain conditions. We consider as a model the case of first order absorbing boundary conditions. Optimal error estimates that hold in natural norms under reasonable assumptions are given, among which lies a typical CFL condition for hyperbolic equations.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
