An explicit P1 finite element scheme for Maxwell's equations with constant permittivity in a boundary neighborhood

Abstract

This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are combined with a well-known explicit finite-difference scheme for the time discretization. The analysis 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 problem-definition domain. Optimal convergence results are established in natural norms under reasonable assumptions, provided a classical CFL condition holds. A numerical validation of the theoretical results is provided.

arXiv commentThis version consists of 38 pages. It incorporates an additional section containing results of numerical experimentation, which validate the theoretical analysis

References in corpus (1)

• Optimization approach for the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions from limited observations

Cited by in corpus (3)

• An adaptive finite element/finite difference domain decomposition method for applications in microwave imaging
• On stabilized P1 finite element approximation fortime harmonic Maxwell's equations
• Numerical validation of an explicit P1 finite-element scheme for Maxwell's equations in a polygon with variable permittivity away from its boundary