Error estimation and adaptivity

Abstract

This chapter is devoted to a posteriori error estimation and adaptivity. Error estimators can help to control the quality of simulation results and serve as stopping criteria for our algorithms. In the following section we will start by gathering the basics of a posteriori error estimation in the finite element method. As we aim at the application to complex problems like fluid-structure interactions, the main target will be efficiency and ease of realization. Error estimation will be based on the Dual Weighted Residual Method, that has been developed by Becker and Rannacher [40, 41] as a very flexible tool to estimate errors in goal functionals of the solution that can be any kind of output values, such as the deformation of a solid-point, the wall stress on an elastic obstacle or the vorticity in a flow field.