6 research outputs found
A Two-Level Method for Mimetic Finite Difference Discretizations of Elliptic Problems
We propose and analyze a two-level method for mimetic finite difference
approximations of second order elliptic boundary value problems. We prove that
the two-level algorithm is uniformly convergent, i.e., the number of iterations
needed to achieve convergence is uniformly bounded independently of the
characteristic size of the underling partition. We also show that the resulting
scheme provides a uniform preconditioner with respect to the number of degrees
of freedom. Numerical results that validate the theory are also presented
Hierarchical a posteriori error estimators for the mimetic discretization of elliptic problems
We present an a posteriori error estimate of hierarchical type for the mimetic discretization of elliptic problems. Under a saturation assumption, the global reliability and efficiency of the proposed a posteriori estimator are proved.
Several numerical experiments assess the actual performance of the local error indicators in driving adaptive mesh refinement algorithms based on different marking strategies. Finally, we analyze and test an inexpensive variant of the proposed error estimator which drastically reduces the overall computational cost of the adaptive procedures
SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES
Crack propagation in thin shell structures due to cutting is conveniently simulated
using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell
elements are usually preferred for the discretization in the presence of complex material
behavior and degradation phenomena such as delamination, since they allow for a correct
representation of the thickness geometry. However, in solid-shell elements the small thickness
leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new
selective mass scaling technique is proposed to increase the time-step size without affecting
accuracy. New ”directional” cohesive interface elements are used in conjunction with selective
mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile
shells