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

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 for a Bernoulli-type free-boundary problem that th...

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 appropriate dual problem (linearized adjoint) is, ...

Goal-oriented Error Estimation for Free-boundary Problems Using the Exact Shape-linearized Adjoint

Since the late 1990s, goal-oriented error estimation and goal-oriented adaptive methods have been developed to control the discretization error in goal functionals of the solution1,2. These methods have mostly been applied to linear and nonlinear problems in solid and fluid mechanics. An important recent development is the extension of goal-oriented adaptive methods to multiphysics problems inv...

Goal - Oriented Error Estimation and Adaptivity for theFinite Element

In this paper, we study a new approach in a posteriori error estimation, in which the numerical error of nite element approximations is estimated in terms of quantities of interest rather than the classical energy norm. These so-called quantities of interest are characterized by linear functionals on the space of functions to where the solution belongs. We present here the theory with respect t...

Goal-oriented error estimation for fast approximations of nonlinear problems