Finite-Element Methods for a Strongly Damped Wave Equation

Publisher Website
Google Scholar
Abstract
Error estimates of optimal order are proved for semidiscrete and completely discrete finite-element methods for a linear wave equation with strong damping, arising in viscoelastic theory. It is demonstrated that the exact solution may be interpreted in terms of an analytic semigroup, and as a result that, although the solution has essentially the spatial regularity of its initial data, it is infinitely differentiable in time for t>0. The estimates for the spatially discrete method are derived by energy arguments. Rational approximation of analytic semigroups is discussed in a general setting, by means of spectral representation, and the results are used to analyse the completely discrete schemes. Both smooth (and compatible) and less smooth data are considered.

This publication has 0 references indexed in Scilit: