Title :

Asymptotic optimality of the edge finite element approximation of the time-harmonic Maxwell's equations

Author(s) :

Chaumont-Frelet, Théophile [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Ern, Alexandre [Auteur]
Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Simulation for the Environment: Reliable and Efficient Numerical Algorithms [SERENA]

English keyword(s) :

Electromagnetics
Finite element methods
Maxwell's equations
Duality argument
Asymptotic optimality

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

We analyze the conforming approximation of the time-harmonic Maxwell's equations using Nédélec (edge) finite elements. We prove that the approximation is asymptotically optimal, i.e., the approximation error in the energy ...
Show more >We analyze the conforming approximation of the time-harmonic Maxwell's equations using Nédélec (edge) finite elements. We prove that the approximation is asymptotically optimal, i.e., the approximation error in the energy norm is bounded by the bestapproximation error times a constant that tends to one as the mesh is refined and/or the polynomial degree is increased. Moreover, under the same conditions on the mesh and/or the polynomial degree, we establish discrete inf-sup stability with a constant that corresponds to the continuous constant up to a factor of two at most. Our proofs apply under minimal regularity assumptions on the exact solution, so that general domains, material coefficients, and right-hand sides are allowed.Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL