In this thesis, we develop, analyze and implement adaptive finite element methods for fully coupled, time-dependent fluid–structure interaction problems and incompressible flows. The presented adaptive methods are based on a posteriori error estimates, where both space discretization and time discretization are adaptively modified based on the solution of an auxiliary linearized dual problem to control the error in a given goal functional of interest. We also include in our analysis the effect of using an inconsistent finite element formulation, such as an operator splitting method, in the computation of the numerical solution. We demonstrate the accuracy and efficiency of the adaptive algorithm with a series of numerical examples.
List of papers. Papers I-III are removed from the thesis due to copyright restrictions.
Kristoffer Selim, Anders Logg, Harish Narayanan, and Mats G. Larson:
An Adaptive Finite Element Method for Fluid–Structure Interaction
Kristoffer Selim, Anders Logg, and Mats G. Larson:
An Adaptive Finite Element Splitting Method for the Incompressible Navier–Stokes Equations
An Adaptive Finite Element Solver for Fluid–Structure Interaction Problems