Space adaptive finite element methods for dynamic Signorini problems

Space Adaptive Finite Element Methods for Dynamic Obstacle Problems

A numerical study on continuous space-time Finite Element Methods for dynamic Signorini problems

Space-time nite element methods for dynamic Signorini problems are discussed in this article. The discretization scheme is based on a mixed space-time formulation of the continuous problem, where the Lagrange multipliers represent the contact stress. To construct the trial space for the displacement and the velocity, we use piecewise polynomial and globally continuous basis functions in space a...

Space Adaptive Finite Element Methods for Dynamic Signorini Problems in the Simulation of the NC-Shape Grinding Process

A simulation of the NC-shape grinding process of free formed surfaces is considered. A central issue in the simulation is the numerical solution of dynamic Signorini problems. Here, space adaptive techniques for such problems are discussed. The Newmark method in time and low order finite elements in space are used for discretisation. For the global discretisation error in space, an a posteriori...

Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems

In this paper we summerize recent results on a posteriori error estimation and adaptivity for space-time finite element discretizations of parabolic optimization problems. The provided error estimates assess the discretization error with respect to a given quantity of interest and separate the influences of different parts of the discretization (time, space, and control discretization). This al...

Adaptive Finite Element Methods for Multiphysics Problems Adaptive Finite Element Methods for Multiphysics Problems

In this thesis we develop and evaluate the performance of adaptive finite element methods for multiphysics problems. In particular, we propose a methodology for deriving computable error estimates when solving unidirectionally coupled multiphysics problems using segregated finite element solvers. The error estimates are of a posteriori type and are derived using the standard framework of dual w...