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Space-time finite element methods for elastodynamics: Formulations and error estimates. (English) Zbl 0616.73063
Space-time finite element methods are developed for classical elastodynamics. The approach employs the discontinuous Galerkin method in time and incorporates stabilizing terms of least-squares type. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Optimal error estimates are predicted, and confirmed numerically, for arbitrary combinations of displacement and velocity interpolations. The procedures developed are easily generalized to structural dynamics and a wide class of second-order hyperbolic problems.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65K10 Numerical optimization and variational techniques
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