Antonopoulou, Dimitra2015-01-192015-01-192015-06-30Antonopoulou, D. (2015). Galerkin methods for a Schroedinger-type equation with a dynamical boundary condition in two dimensions. ESAIM: M2AN, (49)4, 1127-1156. DOI: 10.1051/m2an/20150042822-784010.1051/m2an/2015004http://hdl.handle.net/10034/338552This is the author's PDF version of an article published in ESAIM: M2AN© 2015. The definitive version is available at http://www.esaim-m2an.org/In this paper, we consider a two-dimensional Schodinger-type equation with a dynamical boundary condition. This model describes the long-range sound propagation in naval environments of variable rigid bottom topography. Our choice for a regular enough finite element approximation is motivated by the dynamical condition and therefore, consists of a cubic splines implicit Galerkin method in space. Furthermore, we apply a Crank-Nicolson time stepping for the evolutionary variable. We prove existence and stability of the semidiscrete and fully discrete solution.en2-D Schrodinger equationfinite element methodserror estimatesnoncylindrical domainNeumann boundary conditioncubic splinesCrank-Nicolson time steppingdynamical boundary conditionunderwater acousticsArticle2804-7214ESAIM: M2AN