Mortar element coupling between global scalar and local vector potentials to solve eddy current problems Y. Maday, F. Rapetti, B. I. Wohlmuth Summary. The T - Q formulation of the magnetic field has been introduced in many papers for the approximation of the magnetic quantities modeled by the eddy current equations. This decomposition allows us to use a scalar function in the main part of the computational domain, reducing the use of vector quantities in the conducting parts. We propose here to approximate these two quantities on different and non-matching grids so as. e.g., to tackle a problem where the conducting part can move in the global domain. The connection between the two grids is managed with mortar element tools. The numerical analysis is presented, resulting in error bounds for the solution. 1 Introduction The numerical simulation of low frequency electromagnetic devices can be based on the eddy current model (see [1,2,4]). Two main families of formulations are widely used, one based on magnetic and the other based on electric fields. Here, we restrict ourselves to the magnetic field approach and we extend what was presented briefly in [8]. The entire space ]R3 is decomposed in the conducting region Ve and the external region ]R3 \ Ve. Then, the quasi-stationary Maxwell equations restricted to the conducting region read: '\l x H = I, '\l·B =0, in Ve, (1) where H, B, I and E denote the magnetic field, the magnetic flux density, the current density and the electric field. The densities and the fields are linked by the constitutive properties, i.e., I = 0' E, B = /LH, where /L is the magnetic permeability and 0' :::: 0'0 > 0 stands for the electric conductivity. Moreover, we assume that the material parameters are time independent and associated with a linear isotropic material. In the external insulating region the conductivity is equal to zero and thus we obtain the field equations: '\l x H = Is, '\l·B=O, III V \ Ve, (2) with B = /LH, and the external source Is. We assume that no external source is situated within the conduction regions. The source Is is extended by zero onto ]R3 and still denoted by is. The problem is well posed by imposing regularity conditions at infinity and the interface conditions: [H] x ne = 0, [B] . ne = 0, on aVe, (3) F. Brezzi et al. (Eds.), Numerical Mathematics and Advanced Applications © Springer-Verlag Italia 2003