Volume 56, Number 4, July-August 2022
|Page(s)||1223 - 1253|
|Published online||27 June 2022|
Convergence analysis of a local stationarity scheme for rate-independent systems
Fakultät für Mathematik, Technische Universität Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany
* Corresponding author: email@example.com
Accepted: 6 April 2022
This paper is concerned with an approximation scheme for rate-independent systems governed by a non-smooth dissipation and a possibly non-convex energy functional. The scheme is based on the local minimization scheme introduced in Efendiev and Mielke [J. Convex Anal. 13 (2006) 151–167], but relies on local stationarity of the underlying minimization problem. Under the assumption of Mosco-convergence for the dissipation functional, we show that accumulation points exist and are so-called parametrized BV-solutions of the rate-independent system. In particular, this guarantees the existence of parametrized BV-solutions for a rather general setting. Afterwards, we apply the scheme to a model for the evolution of damage.
Mathematics Subject Classification: 65J08 / 65J15 / 65M60 / 74H15 / 74R05
Key words: Rate independent systems / parametrized BV-solutions / unbounded dissipation / damage evolutions / finite elements / semismooth Newton methods
© The authors. Published by EDP Sciences, SMAI 2022
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