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Applications of Rosenbrock‐type methods to the p‐version of finite elements
Author(s) -
Netz Torben,
Hartmann Stefan,
Hamkar AhmadWahadj
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110119
Subject(s) - discretization , finite element method , backward euler method , diagonal , type (biology) , runge–kutta methods , linear multistep method , mathematics , euler's formula , domain (mathematical analysis) , mathematical analysis , numerical analysis , geometry , physics , differential equation , differential algebraic equation , ecology , ordinary differential equation , biology , thermodynamics
In quasistatic solid mechanics the spatial as well as the temporal domain need to be discetized. For the spatial discretization usually elements with linear shape functions are used even though it has been shown that generally the p ‐version of the finite elemente method yields more effective discretizations, see e.g. [1], [2]. For the temporal discretization diagonal‐implicit, see e.g. [4], and especially linear‐implicit Runge‐Kutta schemes, see e.g. [5], [6], have for smooth problems proven to be superior to the frequently applied Backward‐Euler scheme (BE). Thus an approach combining the p ‐version of the finite element method with linear‐implicit Runge‐Kutta schemes, so‐called Rosenbrock‐type methods, is presented. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)