Computational algorithms for FE formulations involving fractional operators

摘要

This paper considers the development of transient solution algorithms for finite element simulations of viscoelastic problems involving fractional integrodifferential operators. Specifically, numerical approximations are developed for the Grunwald-Liouville-Riemann formalism. This includes establishing formal error estimations. Based on the numerical representations of the fractional operators, implicit, explicit and predictor corrector type transient algorithms are derived for viscoelastic finite element simulations. To illustrate their computational properties, the results of several numerical benchmark experiments are presented. These emphasize the efficiency and stability of the various algorithms developed.