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Semidiscrete and single step fully discrete finite element approximations for second order hyperbolic equations with nonsmooth solutions. (English) Zbl 0766.65082
The author considers finite element approximations for an initial- boundary value problem attached to a second order hyperbolic equation. The spatial operator is a second order uniformly elliptic one.
For semidiscrete approximations and for fully discrete approximations (based on rational approximations of $$\exp(-z))$$ convergence estimates in negative norms are obtained. $$L^ 2$$ projections of the initial data as starting values are used in both cases.

##### MSC:
 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35L15 Initial value problems for second-order hyperbolic equations
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##### References:
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