Galerkin Methods for Parabolic and Schrödinger Equations with Dynamical Boundary Conditions and Applications to Underwater Acoustics

@article{Antonopoulou2009GalerkinMF,
title={Galerkin Methods for Parabolic and Schr{\"o}dinger Equations with Dynamical Boundary Conditions and Applications to Underwater Acoustics},
author={D. C. Antonopoulou and V. A. Dougalis and Georgios E. Zouraris},
journal={SIAM J. Numerical Analysis},
year={2009},
volume={47},
pages={2752-2781}
}

In this paper we consider Galerkin-finite element methods that approximate the solutions of initial-boundary-value problems in one space dimension for parabolic and Schrödinger evolution equations with dynamical boundary conditions. Error estimates of optimal rates of convergence in L 2 and H 1 are proved for the accociated semidiscrete and fully discrete Crank-Nicolson-Galerkin approximations. The problem involving the Schrödinger equation is motivated by considering the standard 'parabolic… CONTINUE READING