Convergence of \(\mathrm{dG}(1)\) in elastoplastic evolution
type: Item
instance of: scholarly article
title: Convergence of \(\mathrm{dG}(1)\) in elastoplastic evolution
zbMATH Open document ID: 1433.65283
author: C. Carstensen
author: Dongjie Liu
author: Jochen Alberty
published in: Numerische Mathematik
publication date: 2019-02-21T00:00:00Z
review text: The discontinuous Galerkin time discretization, abbreviated as dG(\(k\)), with a polynomial degree at most \(k\in \mathbb{N}_0\) of elastoplastic evolution problems is discussed. The paper has the following structure. Section 1 is an introduction and overview. Section 2 is devoted to the strong form of a model example in elastoplasticity with hardening and the weak primal and dual form. The resulting fully discrete scheme is a variational inequality at each time-step and it is given in Section 3. The equivalence of two discrete formulations, the dual and the primal one, is given in this section. The error analysis in Section 4 explains and verifies the asymptotic convergence result. In Section 5, the numerical investigation for a benchmark problem with known analytic solution provides empirical evidence of a higher convergence rate of the dG(1) scheme compared to dG(0).
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 74C05
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65M60
zbMATH DE Number: 7027402
zbMATH Keywords: elastoplastic evolution
zbMATH Keywords: discontinuous Galerkin method
zbMATH Keywords: fully discrete scheme
reviewed by: Temur Jangveladze
MaRDI profile type: Publication
full work available at URL: s00211-018-0999-6
OpenAlex ID: W2894100441
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DOI: 10.1007/S00211-018-0999-6
description: scientific article; zbMATH DE number 7027402