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...

Goal-oriented-error estimation for hierarchical models of a different type

For the simulation of many physical processes, a collection of mathematical models with different level of sophistication is available. Such a collection is called a class of hierarchical models in which the hierarchy is determined by the level of sophistication of the models. In many such classes, solving a fine model is computationally...

Aspects of goal-oriented model-error estimation in convection-diffusion problems

For goal-oriented model adaptation a model-error estimator is required to drive the adaptation process. In recent years publications have appeared on the dual-weighted residual (DWR) method in the application of model-error estimation in output functionals. In this paper we study the application of the DWR method for convection-diffusion...

Aspects of goal-oriented model-error estimation in convection-diffusion problems

For goal-oriented model adaptation a model-error estimator is required to drive the adaptation process. In recent years publications have appeared on the dual-weighted residual (DWR) method in the application of model-error estimation in output functionals. In this paper we study the application of the DWR method for convection-diffusion...

Dual-based a-posteriori error estimation for fluid-structure interaction by the embedded-domain method

Numerical simulations of fluid-structure interaction typically require vast computational resources. Finite-element techniques employing goal-oriented hp-adaptation strategies could offer a substantial improvement in the efficiency of such simulations. These strategies rely on dual-based a-posteriori error estimates for quantities of interest....

Dual-based a-posteriori error estimation for fluid-structure interaction by the embedded-domain method

Numerical simulations of fluid-structure interaction typically require vast computational resources. Finite-element techniques employing goal-oriented hp-adaptation strategies could offer a substantial improvement in the efficiency of such simulations. These strategies rely on dual-based a-posteriori error estimates for quantities of interest....