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 present a framework for the construction of a globally C 1-smooth isogeometric spline
space over a particular class of G 1-smooth multi-patch surfaces called analysis-suitable G 1 …

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 …

We propose and analyze novel adaptive algorithms for the numerical solution of elliptic
partial differential equations with parametric uncertainty. Four different marking strategies …

We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh
procedures for the finite element method that are based on the localization of a posteriori …

In this work, we introduce a novel hp-adaptive strategy. The main goal is to minimize the
complexity and implementational efforts hence increasing the robustness of the algorithm …

The paper considers a class of parametric elliptic partial differential equations (PDEs),
where the coefficients and the right-hand side function depend on infinitely many (uncertain) …

The development of the world cannot be separated from energy: the energy crisis has
become a major challenge in this era, and nuclear energy has been applied to many fields …

In simulation of heat conduction with temperature-independent physical properties and
boundary conditions (BCs), Galerkin residual analysis and variational analysis yield …

We consider an adaptive finite element method with arbitrary but fixed polynomial degree
p≥ 1, where adaptivity is driven by an edge-based residual error estimator. Based on the …