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A dynamic thermoviscoelastic problem: numerical analysis and computational experiments. (English) Zbl 1248.74008
Summary: We consider the numerical analysis of a dynamic problem which models the temperature evolution in a thermoviscoelastic body. The variational problem is formulated as a coupled system of evolutionary nonlinear variational equations. An existence and uniqueness result is recalled. Then, a fully discrete numerical scheme is introduced by using the finite element method to approximate the spatial variable, and an Euler scheme to discretise the time derivatives. Error estimates are derived and, under suitable regularity assumptions, the linear convergence of the numerical scheme is obtained. Finally, the results of simulations of some two-dimensional numerical examples are presented to demonstrate the accuracy of the algorithm and the behaviour of the solution.

MSC:
74D10 Nonlinear constitutive equations for materials with memory
74H20 Existence of solutions of dynamical problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74S20 Finite difference methods applied to problems in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
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