Basics and some applications of the mortar element method

We describe the main characteristics of the mortar element method, together with the usual arguments for its numerical analysis in an abstract framework. We illustrate this presentation by focussing on mortar spectral element and mortar finite element methods. We give three examples of recent applications, concerning the treatment of non homogeneous media, eddy currents in moving conductors, and finite element mesh adaptivity. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)