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High‐Order Time Integration in the p‐Version of Finite Elements
Author(s) -
Netz Torben,
Hartmann Stefan
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010093
Subject(s) - discretization , diagonal , backward euler method , finite element method , euler's formula , domain (mathematical analysis) , mathematics , spacetime , legendre polynomials , space (punctuation) , isothermal process , time domain , order (exchange) , mathematical analysis , computer science , geometry , physics , finance , quantum mechanics , economics , computer vision , thermodynamics , operating system
In isothermal solid mechanics, the space and time domain need to be discretized. This paper presents an approach using high‐order finite elements based on Legendre polynomials for the spatial discretization and time‐adaptive diagonal‐implicit Runge‐Kutta methods for the temporal discretization. The superiority of this approach over a traditional one using linear shape functions for the space domain and a Backward‐Euler scheme for the time domain is demonstrated. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)