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Finite element Galerkin solutions for the strongly damped extensible beam equations. (English) Zbl 1082.65571
Summary: Finite element Galerkin solutions for the strongly damped extensible beam equations are considered. A semidiscrete scheme and a fully discrete time Galerkin method are studied and the corresponding stability and error estimates are obtained. Ratios of numerical convergence are given.

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74S05 Finite element methods applied to problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
35A35 Theoretical approximation in context of PDEs
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