Goal-Oriented Error Estimation and Adaptivity for Free-Boundary Problems: The Shape-Linearization Approach

We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems via shape-linearization principles. To derive an appropriate dual (linearized adjoint) problem, we linearize the domain dependence of the very weak form and goal functional of interest using techniques from shape calculus. We show...

Goal-Oriented Error Estimation and Adaptivity for Free-Boundary Problems: The Domain-Map Linearization Approach

In free-boundary problems, the accuracy of a goal quantity of interest depends on both the accuracy of the approximate solution and the accuracy of the domain approximation. We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems that include both sources of error. The derivation of an...

Goal-Adaptive Discretization of Fluid-Structure Interaction

The simulation of complex physical phenomena, such as fluid–structure interaction, appears to be within reach in view of the significant progress in computing power over the last decades. Yet, we are still far away from what is desirable in an evermore-demanding, science-and-technology-based society. If, however, we are modest with what we need...