https://hal.science/hal-01853643Bécache, ElianeElianeBécachePOEMS - Propagation des Ondes : Étude Mathématique et Simulation - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique - UMA - Unité de Mathématiques Appliquées - ENSTA Paris - École Nationale Supérieure de Techniques Avancées - CNRS - Centre National de la Recherche ScientifiqueRodríguez Garcia, JerónimoJerónimoRodríguez GarciaUSC - Universidade de Santiago de Compostela [Spain]Departamento de Matemática Aplicada - USC - Universidade de Santiago de Compostela [Spain]Tsogka, ChrysoulaChrysoulaTsogkaUC Merced - University of California [Merced] - UC - University of CaliforniaThe fictitious domain method and applications in wave propagationHAL CCSD2009fictitious domain methodmixed finite elementscrackselastic wavesacoustic waves[MATH] Mathematics [math][MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]Becache, Eliane2018-08-03 15:01:092023-03-24 14:53:072018-08-03 16:53:35enBook sectionsapplication/pdf1This paper deals with the convergence analysis of the fictitious domain method used for taking into account the Neumann boundary condition on the surface of a crack (or more generally an object) in the context of acoustic and elastic wave propagation. For both types of waves we consider the first order in time formulation of the problem known as mixed velocity-pressure formulation for acoustics and velocity-stress formulation for elastodynamics. The convergence analysis for the discrete problem depends on the mixed finite elements used. We consider here two families of mixed finite elements that are compatible with mass lumping. When using the first one which is less expensive and corresponds to the choice made in a previous paper, it is shown that the fictitious domain method does not always converge. For the second one a theoretical convergence analysis was carried out in [7] for the acoustic case. Here we present numerical results that illustrate the convergence of the method both for acoustic and elastic waves.