Finite-Element Methods for a Strongly Damped Wave Equation |
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Authors: | LARSSON STIG; THOM?E VIDAR; WAHLBIN LARS B |
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Institution: |
Department of Mathematics, Chalmers University of Technology S-412 96 G?teborg, Sweden
Department of Mathematics, White Hall, Cornell University Ithaca, NY 14853, USA
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Abstract: | Error estimates of optimal order are proved for semidiscreteand completely discrete finite-element methods for a linearwave equation with strong damping, arising in viscoelastic theory.It is demonstrated that the exact solution may be interpretedin terms of an analytic semigroup, and as a result that, althoughthe solution has essentially the spatial regularity of its initialdata, it is infinitely differentiable in time for t>0. Theestimates for the spatially discrete method are derived by energyarguments. Rational approximation of analytic semigroups isdiscussed in a general setting, by means of spectral representation,and the results are used to analyse the completely discreteschemes. Both smooth (and compatible) and less smooth data areconsidered. |
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