Edge elements on anisotropic meshes and approximation of the Maxwell equations. (English) Zbl 1001.65122

Nicaise, Serge

SIAM J. Numer. Anal. 39, No. 3, 784-816 (2001).

This paper concerns some edge element methods on a class of anisotropic meshes based on tetrahedra and prismatic elements. Anisotropic local interpolation error estimates are derived for these types of elements. In particular, the numerical approximation of the Maxwell equations in domains with edges is investigated. Some numerical tests are given.

Reviewer: Laura-Iulia Aniţa (Iaşi)

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q60	PDEs in connection with optics and electromagnetic theory
78A30	Electro- and magnetostatics
78M10	Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N15	Error bounds for boundary value problems involving PDEs
65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs

Keywords:

anisotropic mesh; edge element; anisotropic interpolation; error estimate; Maxwell equations; edge singularity; numerical examples