Mathematical Models and Methods in Applied Sciences c  World Scientific Publishing Company TWO DISCRETIZATION SCHEMES FOR A TIME-DOMAIN DISSIPATIVE ACOUSTICS PROBLEM ALFREDO BERM ´ UDEZ Departamento de Matem´ atica Aplicada Universidade de Santiago de Compostela 15706 Santiago de Compostela, Spain mabermud@usc.es RODOLFO RODR ´ IGUEZ GI 2 MA, Departamento de Ingenier´ ıa Matem´ atica Universidad de Concepci´ on Casilla 160-C, Concepci´ on, Chile rodolfo@ing-mat.udec.cl DUARTE SANTAMARINA Departamento de Matem´ atica Aplicada Universidade de Santiago de Compostela 15706 Santiago de Compostela, Spain duartesr@usc.es This paper deals with a time-domain mathematical model for dissipative acoustics and is organized as follows. First, the equations of this model are written in terms of dis- placement and temperature fields and an energy equation is obtained. The resulting initial-boundary value problem is written in a functional framework allowing us to prove the existence and uniqueness of solution. Next, two different time-discretization schemes are proposed, and stability and error estimates are proved for both. Finally, numerical results are reported which were obtained by combining these time-schemes with La- grangian and Raviart-Thomas finite elements for temperature and displacement fields, respectively. Keywords : Dissipative acoustics; time-domain problems; time-discretization schemes; fi- nite elements AMS Subject Classification: 65M12, 65M15, 65M60, 76M10 1. Introduction Although dissipation is usually neglected in standard acoustics, modeling this phe- nomenon is absolutely essential in order to study the effect of noise reduction tech- niques. Indeed, in most real situations damping mechanisms that transform mechan- ical energy into heat do exist. Sometimes these mechanisms are based on surface damping arising from viscoelastic materials placed on the boundary of the propa- gation domain. In these cases, the dissipative effects are included in the model by 1