PhD Defence: Fast Solvers and Adaptive High-Order FEM in Elastoplasticity

Fast Solvers and Adaptive High-Order FEM in Elastoplasticity

In his PhD defense, the author summarizes the most important results of his thesis: On the one hand, a new framework has been developed in the scope of analyzing and and numerically solve elastoplastic problems. In difference to classical solvers, the investigated approach yields a minimization problem with respect to the displacement variable, only. Under a weak integrability assumtion, a Newton-like method can be shown to converge super-linearly for the obtained minimization problem - a fact which has already been observed with similar elastoplastic solvers, but never proved in earlier literature. On the other hand, the discretization of an elastoplastic problem by means of various adaptive hp-FEM strategies is studied and illustrated by numerical examples.