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A 1-D model of a slab of glass of a small thickness is considered. The governing equations are those of the classical 1-D linear viscoelasticity. A load due to the temperature gradients is assumed. The aim is to model the process called annealing. It is shown that an additional load due to structural strain is crucial for the success of the model. Algorithms of a numerical solution of the governing equations are proposed. Numerical results are presented and commented.
The aim of the paper is to derive a method for the construction of a-posteriori error estimate to approximate solutions to parabolic initial-boundary value problems. The computation of the suggested error bound requires only the computation of a finite number of systems or linear algebraic equations. These systems can be solved parallelly. It is proved that the suggested a-posteriori error estimate tends to zero if the approximation tends to the true solution.
Numerical simulations of time-dependent behaviour of advances structures need the analysis of systems of partial differential equations of hyperbolic type, whose semi-discretization, using the Fourier multiplicative decomposition together with the finite element or similar techniques, leads to large sparse systems of ordinary differential equations. Effective and robust methods for numerical evaluation of their solutions in particular time steps are required; thus still new computational schemes...
We consider a heat equation with a non-linear right-hand side which depends on certain Volterra-type functionals. We study the problem of existence and convergence for the method of lines by means of semi-discrete inverse formulae.
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