Maxwell's equations in composite materials: remarks on density

In this Note, a necessary and sufficient condition is found, which guarante es the density of piecewise regular vector fields in the subspace of H(curl ; Omega) whose elements satisfy div(epsilon E) is an element of L-2(Omega 2 ) and have their tangential trace in L-2(partial derivative Omega); Omega b eing a polygonal domain of R-2, union of J polygonal subdomains. The proof uses explicitly the singularities of a scalar transmission problem. Numeric ally the result allows a discretization of Maxwell's equations with an impe dance boundary condition in composite materials by means of nodal, H-1-conf orming, finite elements. (C) 2000 Academie des sciences/Editions scientifiq ues et medicales Elsevier SAS.