Abstract
Under the leadership of Professor Stephan, four PhD projects were investigated during the running period of the GRK615 on the field of error controlled finite element/boundary element methods, namely on adaptive FE/BE couplings for transmission problems in elasticity (S. Oestmann) and for fluid-structure interaction (C. Domínguez) and on contact problems with friction (A. Chernov) as well as with delamination (L. Nesemann).
The Galerkin coupling formulations in Sections 1 and 4 are based on the fundamental paper by Costabel and Stephan [7], whereas the least squares coupling approach - applicable to mixed formulations and avoiding locking - extends the results of Maischak and Stephan [15]. The presented a posteriori error estimates for the h-version coupling extends those from Carstensen and Stephan [2, 3]. Contact problems with friction are considered with non-matching grids on the contact boundary and the foundation in Section 3. With mortar techniques, formulations are derived for a variational inequality on the contact boundary with the Poincaré- Steklov operator (Dirichlet-to-Neumann map), and the hp-version is analyzed and implemented for better numerical simulation [5]; penalty formulations are investigated in [4]. For adhesion problems (delamination) leading to a hemivariational inequality due to the set-valued adhesion law, existence and uniqueness results for the solution, representing the displacement, are given in Section 2 from [16]. Here, the bundle-Newton algorithm is used as a solver for the discrete finite element system and numerical simulations are given with a heuristic refinement algorithm, based on a residual-type error estimator.
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References
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Stephan, E.P. (2011). Finite Element and Boundary Element Approaches to Transmission and Contact Problems in Elasticity. In: Stephan, E., Wriggers, P. (eds) Modelling, Simulation and Software Concepts for Scientific-Technological Problems. Lecture Notes in Applied and Computational Mechanics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20490-6_7
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DOI: https://doi.org/10.1007/978-3-642-20490-6_7
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