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On mixed finite element methods for linear elastodynamics. (English) Zbl 0734.73074

Summary: We construct and analyze finite element methods for approximating the equations of linear elastodynamics, using mixed elements for the discretization of the spatial variables. We consider two different mixed formulations for the problem and analyze semidiscrete and up to fourth- order in time fully discrete approximations. \(L^ 2\) optimal-order error estimates are proved for the approximations of displacement and stress.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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References:

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