Variable Time-Step θ-Scheme for Nonlinear Second Order Evolution Inclusion

Variable Time-Step θ-Scheme for Nonlinear Second Order Evolution Inclusion

Year:    2017

International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 6 : pp. 842–868

Abstract

We deal with a multivalued second order dynamical system involving a Clarke subdifferential of a locally Lipschitz functional. We apply a time discretization procedure to construct a sequence of solutions to a family of the approximate problems and show its convergence to a solution of the exact problem as the time step size vanishes. We consider a nonautonomous problem in which both the viscosity and the multivalued operators depend on time explicitly. The time discretization method we use, is the $\theta$-scheme with $\theta \in [\frac{1}{2}, 1]$, thus, in particular, the Crank-Nicolson scheme and the implicit Euler scheme are included. We apply our result to a class of dynamic hemivariational inequalities.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2017-IJNAM-10483

International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 6 : pp. 842–868

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Clarke subdifferential hemivariational inequality second order inclusion time discretization numerical methods.