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.
Author: | Carsten Carstensen, Simone Hock, Jochen Alberty |
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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 |