Open Access
| Issue |
ESAIM: M2AN
Volume 60, Number 4, July-August 2026
|
|
|---|---|---|
| Page(s) | 1769 - 1803 | |
| DOI | https://doi.org/10.1051/m2an/2026042 | |
| Published online | 03 August 2026 | |
- A. Beni Hamad, G. Beck, S. Imperiale andP. Joly, An efficient numerical method for time domain electromagnetic wave propagation in co-axial cables. Comput. Methods Appl. Math. 22 (2022) 861–888. [Google Scholar]
- D.N. Arnold, F. Brezzi, B. Cockburn andL.D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2002) 1749–1779. [CrossRef] [Google Scholar]
- G. Beck, Modëlisation et ëtude mathëmatique de rëseaux de câbles ëlectriques. Thëse de doctorat. Universitë Paris-Saclay (2016). [Google Scholar]
- G. Beck, S. Imperiale andP. Joly, Mathematical modelling of multi conductor cables. Discrete Contin. Dyn. Syst. Ser. S 8 (2015) 521–546. [Google Scholar]
- M. Bergot andM. Duruflé, High-order optimal edge elements for pyramids, prisms and hexahedra. J. Comput. Phys. 232 (2013) 189–213. [Google Scholar]
- A. Burel, S. Imperiale andP. Joly, Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition. Numer. Anal. Appl. 5 (2012) 136–143. [Google Scholar]
- J. Chabassier andS. Imperiale, Space/time convergence analysis of a class of conservative schemes for linear wave equations. C. R. Math. 355 (2017) 282–289. [CrossRef] [MathSciNet] [Google Scholar]
- J. Chabassier andS. Imperiale, Fourth-order energy-preserving locally implicit time discretization for linear wave equations. Int. J. Numer. Methods Eng. 106 (2015) 593–622. [Google Scholar]
- J.-L. Coulomb, F.-X. Zgainski andY. Marechal, A pyramidal element to link hexahedral, prismatic and tetrahedral edge finite elements. Institute of Electrical and Electronics Engineers 33 (1997) 1362–1365. [Google Scholar]
- R. Dautray andJ.L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 1. Springer-Verlag (1990). [Google Scholar]
- S. Descombes, S. Lanteri andL. Moya, Locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell’s equations. J. Sci. Comput. 56 (2013) 190–218. [CrossRef] [MathSciNet] [Google Scholar]
- M. Grote, A. Schneebeli andD. Schötzau, Discontinuous Galerkin finite element method for the wave equation. SIAM J. Numer. Anal. 44 (2006) 2408–2431. [Google Scholar]
- M. Grote, A. Schneebeli andD. Schötzau, Interior penalty discontinuous Galerkin method for Maxwell’s equations: energy norm error estimates. J. Comput. Appl. Math. 204 (2007) 375–386. [Google Scholar]
- M. Grote, A. Schneebeli andD. Schötzau, Interior penalty discontinuous Galerkin method for Maxwell’s equations: optimal L 2-norm error estimates. IMA J. Numer. Anal. 28 (2008) 440–468. [Google Scholar]
- M. Hochbruck, T. Jahnke andR. Schnaubelt, Convergence of an ADI splitting for Maxwell’s equations. Numer. Math. 129 (2014) 535–561. [Google Scholar]
- M. Hochbruck andJ. Leibold, An implicit-explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions. Numer. Math. 147 (2021) 869–899. [CrossRef] [MathSciNet] [Google Scholar]
- M. Hochbruck andA. Sturm, Error analysis of a second-order locally implicit method for linear Maxwell’s equations. SIAM J. Numer. Anal. 54 (2016) 3167–3191. [CrossRef] [MathSciNet] [Google Scholar]
- P. Houston, I. Perugia, A. Schneebeli andD. Schötzau, Interior penalty method for the indefinite time-harmonic Maxwell equations. Numer. Math. 100 (2005) 485–518. [Google Scholar]
- S. Imperiale andP. Joly, Error estimates for 1D asymptotic models in coaxial cables with non-homogeneous cross-section. Adv. Appl. Math. Mech. 4 (2012) 647–664. [Google Scholar]
- S. Imperiale andP. Joly, Mathematical modeling of electromagnetic wave propagation in heterogeneous lossy coaxial cables with variable cross-section. Appl. Numer. Math. 79 (2014) 42–61. [Google Scholar]
- S. Imperiale, Modëlisation mathëmatique et numërique de capteurs piëzoëlectriques. Thëse de doctorat, Paris IX (2012). [Google Scholar]
- A. Kameni, F. Loete, S. Ziani, K. Kahalerras andL. Pichon, Time domain modeling of soft faults in wiring system by a nodal Discontinuous Galerkin Method with high-order hexahedral meshes. in Proc. of the IEEE International Conference on the Computation of Electromagnetic Fields (2015). [Google Scholar]
- J. Lee andB. Fornberg, A split step approach for the 3-D Maxwell’s equations. J. Comput. Appl. Math. 158 (2003) 485–505. [Google Scholar]
- J. Lee andB. Fornberg, Some unconditionally stable time stepping methods for the 3D Maxwell’s equations. J. Comput. Appl. Math. 166 (2004) 497–523. [Google Scholar]
- J. Li, E. Machorro andS. Shields, Numerical study of signal propagation in corrugated coaxial cables. J. Comput. Appl. Math. 309 (2017) 230–243. [Google Scholar]
- P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford University Press, Oxford (2003). [Google Scholar]
- P. Monk andG.R. Richter, A discontinuous Galerkin method for linear symmetric hyper-bolic systems in inhomogeneous media. J. Sci. Comput. 22–23 (2005) 443–477. [Google Scholar]
- J.C. Nëdëlec, Mixed finite elements in ℝ3. Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet] [Google Scholar]
- T. Rylander andA. Bondeson, Stability of explicit-implicit hybrid time-stepping schemes for Maxwell’s equations. J. Comput. Phys. 179 (2002) 426–438. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.
