Authors: Meyer, Christian
Sievers, Michael
Title: Finite Element Discretization of Local Minimization Schemes for Rate-Independent Evolutions
Language (ISO): en
Abstract: This paper is concerned with a space-time discretization of a rate-independent evolution governed by a non-smooth dissipation and a non-convex energy functional. For the time discretization, we apply the local minimization scheme introduced in [EM06], which is known to resolve time discontinuities, which may show up due to the non-convex energy. The spatial discretization is performed by classical linear finite elements. We show that accumulation points of the sequence of discrete solutions for mesh size tending to zero exist and are so-called parametrized solutions of the continuous problem. The discrete problems are solved by means of a mass lumping scheme for the non-smooth dissipation functional in combination with a semi-smooth Newton method. A numerical test indicates the efficiency of this approach. In addition, we compared the local minimization scheme with a time stepping scheme for global energetic solutions, which shows that both schemes yield different solutions with differing time discontinuities.
Subject Headings: rate independent evolutions
parametrized solutions
finite elements
semi-smooth Newton methods
URI: http://hdl.handle.net/2003/37960
http://dx.doi.org/10.17877/DE290R-19945
Issue Date: 2019-03
Appears in Collections:Ergebnisberichte des Instituts für Angewandte Mathematik

Files in This Item:
File Description SizeFormat 
Ergebnisbericht Nr. 599.pdfDNB1.78 MBAdobe PDFView/Open


This item is protected by original copyright



Items in Eldorado are protected by copyright, with all rights reserved, unless otherwise indicated.