In electromagnetic compatibility (EMC) context, we are interested in developing new accurate methods to solve efficiently and accurately Maxwell's equations in the time domain. Indeed, usual methods such as FDTD or FVTD present important dissipative and/or dispersive errors which prevent to obtain a good numerical approximation of the physical solution for a given industrial scene unless we use a mesh with a very small cell size. To avoid this problem, schemes like the Discontinuous Galerkin (DG) method, based on higher order spatial approximations, have been introduced and studied on unstructured meshes. However the cost of this kind of method can become prohibitive according to the mesh used. In this paper, we first present a higher order spatial approximation method on cartesian meshes. It is based on a finite element approach and recovers at the order 1 the well-known Yee's scheme. Next, to deal with EMC problem, a nonoriented thin wire formalism is proposed for this method. Finally, several examples are given to present the benefits of this new method by comparison with both Yee's scheme and DG approaches.

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