In this chapter, various numerical examples are presented that demonstrate the numerical performance of the a posteriori error estimators developed in this monograph for both the finite and linearized hyperelasticity problems and the Poisson problem. For the energy norm and related error estimators, examples with different types of singularities are considered. The goal-oriented error estimators are primarily applied to linear and nonlinear elastic fracture mechanics problems, including crack propagation, because the J-integral, as a fracture criterion, serves as a numerically challenging nonlinear quantity of particular engineering interest. The numerical methods considered in this chapter are the conventional, mixed, dual-mixed, and extended finite element methods, the finite element method based on stabilized conforming nodal integration (SCNI), and the element-free Galerkin and reproducing kernel particle methods. Various materials, such as concrete and aluminum, are investigated in this chapter with an emphasis on glass and rubber. Although these materials seem to exhibit different material behavior, they share many similarities.
- Brink, U.: Adaptive gemischte finite Elemente in der nichtlinearen Elastostatik und deren Kopplung mit Randelementen. Ph.D. thesis, Forschungs- und Seminarberichte aus dem Bereich der Mechanik der Universität Hannover, Hannover (1998)Google Scholar