Convergence of the finite element method is obtained by a systematic extension of the Ansatz spaces approximating a given mathematical model. The classical h-version extends the approximation by (uniform or adaptive) mesh refinement using a fixed polynomial degree in each element. The pversion keeps the mesh fixed and increases the element polynomial degree, where again uniform or adaptive methods can be applied. The r-method reallocates nodes and elements and adjusts (if high order elements are used) the geometric shape of element edges and faces to certain criteria. All of the three methods (h-, p-, r-extension) can be combined in order to achieve optimized control over approximation error and computational resources. We will characterize these methods in this paper and compare their performance on benchmark problems for elasto-plastic computation. Rate independent as well as rate dependent elastoplastic problems will be investigated in two as well as three dimensions and it will be shown that an exponential rate of convergence can be obtained by a combination of r- and p-methods. Finally, we will give guidelines for practical computation using lower order elements as they are available in commercial finite element codes.     «

Convergence of the finite element method is obtained by a systematic extension of the Ansatz spaces approximating a given mathematical model. The classical h-version extends the approximation by (uniform or adaptive) mesh refinement using a fixed polynomial degree in each element. The pversion keeps the mesh fixed and increases the element polynomial degree, where again uniform or adaptive methods can be applied. The r-method reallocates nodes and elements and adjusts (if high order elements are...     »