COMPDYN 2011 ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis, V. Plevris (eds.) Corfu, Greece, 25-28 May 2011 NON-CONFORMING SPECTRAL APPROXIMATIONS FOR THE ELASTIC WAVE EQUATION IN HETEROGENEOUS MEDIA I. Mazzieri 1,3 , C. Smerzini 2 , P.F. Antonietti 1 , F. Rapetti 3 , M. Stupazzini 4 , R. Paolucci 2 and A. Quarteroni 1,5 1 MOX - Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano, P.za Leonardo da Vinci, 32, 20133 Milano, Italy. e-mail: ilario.mazzieri@mail.polimi.it, paola.antonietti@polimi.it 2 Department of Structural Engineering, Politecnico di Milano P.za Leonardo da Vinci, 32, 20133 Milano, Italy. e-mail: csmerzini@stru.polimi.it 3 Universit´ e de Nice Sophia Antipolis, Laboratoire de Math´ ematiques J.A. Dieudonn´ e, Parc Valrose, Cedex 02, 06108 Nice, France. frapetti@unice.fr 4 Munich RE, K¨ oniginstr. 107, 80802 Munich, Germany. MStupazzini@munichre.com 5 Chair of Modelling and Scientific Computing (CMCS), Mathematics Institute of Computational Science and Engineering (MATHICSE), ´ Ecole Polytechnique F´ ed´ erale de Lausanne (EPFL), Station 8, 1015 Lausanne, Switzerland. alfio.quarteroni@epfl.ch Keywords: Computational seismology, Non-conforming approximations, Mortar Spectral Ele- ment Method, Discontinuous Galerkin Spectral Element Method. Abstract. Non-conforming techniques as the Mortar spectral Element Method (MSEM) or the Discontinuous Galerkin Spectral Element Method (DGSEM) are variational approaches to discretize partial differential equations, that rely on a spectral finite element approximation of a non-overlapping subdomain partition of the computational domain. In this contribution we compare and analyse MSEM and DGSEM, giving more details on the algorithmic aspects of the two non-conforming approaches, and we address their applicability and flexibility to handle seismic wave propagation problems. The numerical strategies are implemented in the spectral elements based code GeoELSE [14]. 1