This work reviews goal-oriented a posteriori error control, adaptivity and solver control for
finite element approximations to boundary and initial-boundary value problems for stationary …

We introduce the concept of machine-learning minimal-residual (ML-MRes) finite element
discretizations of partial differential equations (PDEs), which resolve quantities of interest …

In this work, we derive two-sided a posteriori error estimates for the dual-weighted residual
(DWR) method. We consider both single and multiple goal functionals. Using a saturation …

In this work, we develop adaptive schemes using goal-oriented error control for a highly
nonlinear flow temperature model with temperature dependent density. The dual-weighted …

In this work, we further develop multigoal-oriented a posteriori error estimation with two
objectives in mind. First, we formulate goal-oriented mesh adaptivity for multiple functionals …

We consider goal-oriented adaptive space-time finite-element discretizations of the
regularized parabolic p-Laplace problem on completely unstructured simplicial space-time …

We derive a unified framework for goal-oriented a posteriori estimation covering in particular
higher-order conforming, nonconforming, and discontinuous Galerkin finite element …

The finite‐element method (FEM) is a well‐established procedure for computing
approximate solutions to deterministic engineering problems described by partial differential …

The cost-and memory-efficient finite element simulation of multi-physics problems remains a
challenging task. Goal-oriented space and time adaptive methods derived from the dual …

In this paper, we introduce, analyze, and numerically illustrate a method for taking into
account quantities of interest during the finite element treatment of a boundary-value …