Abstract
This chapter discusses generalization of the finite element method for solution of hyperbolic equations. The finite element method was originally developed for the solution of boundary value problems for elliptic partial differential equations. A natural generalization of the method is to the solution of time-dependent problems, for example, to the solution of parabolic and hyperbolic differential equations. Then very often a finite element discretization is used for space variables, with the finite difference discretization in time. This chapter develops another generalization of the finite element method for the solution of linear time dependent problems using the Laplace transformation for the time variable. It deals with the variational formulation, and proves the convergence of this method for hyperbolic equations of viscoelastic plates.
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