Abstract
In Sect. 3.1, an abstract coupled problem is considered and a few theorems related to the estimation of the accuracy of the Bubnov-Galerkin method are formulated and proved. The error estimates hold for a system of differential equations of a rather general form with homogeneous boundary conditions, which corresponds to coupled thermoelastic problems for plates and shallow shells with variable thickness. In addition, a particular case of this problem (with nonhomogeneous initial conditions), where a prior estimate of the errors of the Bubnov-Galerkin method is most effective, is illustrated and discussed. Finally, a prior estimate for the Bubnov-Galerkin method to a problem generalizing a class of dynamical problems of elasticity (without a heat transfer equation) for both three-dimensional and thin-walled elements of structures is given.
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© 2003 Springer-Verlag Berlin Heidelberg
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Awrejcewicz, J., Krys’ko, V.A. (2003). Estimation of the Errors of the Bubnov-Galerkin Method. In: Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells. Scientific Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55677-7_3
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DOI: https://doi.org/10.1007/978-3-642-55677-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62869-6
Online ISBN: 978-3-642-55677-7
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