Applications of Rosenbrock‐type methods to the p‐version of finite elements

Abstract

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)