Error estimates for the semidiscrete finite-element approximation of a damped wave equation with a smoothing property

摘要

Error estimates are given for the semidiscrete finite-element approximation of an inhomogeneous wave equation, damped by a constant times the positive square root of the elliptic operator in the wave equation times the time derivative of the solution. The damping term smooths the solution. The smoothing property is used to obtain higher-order error estimates for positive time, even when the initial data are non-smooth.