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Convergence Of dG(1) In Elastoplastic Evolution

Please always quote using this URN:urn:nbn:de:0296-matheon-4975
  • The discontinuous Galerkin (dG) method provides a hierarchy of time discretization schemes for evolutionary problems. A dG time discretization has been proposed for a variational inequality in the context of rate-independent inelastic material behaviour in [Alberty, Carstensen: Discontinuous {G}alerkin Time Discretization in Elastoplasticity: Motivation, Numerical Algorithms and Applications, Comp. Meth. Appl. Mech. Engrg. \textbf{191} (2002)] with the help of duality in convex analysis to justify certain jump terms. Convincing numerical experiments have already been displayed in the literature.\This paper establishes a mathematical a~priori error analysis for the dG($1$) scheme with discontinuous piecewise linear polynomials in the temporal and first-order finite elements for the spacial discretization. One novel key idea in the a~priori convergence analysis is an optimal trace estimate under convex constraints. The numerical investigation of the empirical convergence rate in a benchmark concludes the paper.

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Metadaten
Author:Carsten Carstensen, Simone Hock, Jochen Alberty
URN:urn:nbn:de:0296-matheon-4975
Referee:Andreas Griewank
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/03/30
Release Date:2008/03/25
Tag:
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65-XX NUMERICAL ANALYSIS / 65Rxx Integral equations, integral transforms / 65R20 Integral equations
Preprint Number:503
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