Adaptive Finite Element Methods for Fluid-Structure Interaction and Incompressible Flow

Abstract

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.