We formulate and analyze a goal-oriented adaptive finite element method for a semilinear
elliptic PDE and a linear goal functional. The discretization is based on finite elements of …

We provide an abstract framework for optimal goal-oriented adaptivity for finite element
methods and boundary element methods in the spirit of [C. Carstensen et al., Comput. Math …

We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and
analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh …

Since the advent of isogeometric analysis (IGA) in 2005, the finite element method (FEM)
and the boundary element method (BEM) with splines have become an active field of …

We consider a linear elliptic PDE and a quadratic goal functional. The goal-oriented
adaptive FEM algorithm (GOAFEM) solves the primal as well as a dual problem, where the …

We analyze a goal-oriented adaptive algorithm that aims to efficiently compute the quantity
of interest G (u⋆) with a linear goal functional G and the solution u⋆ to a general second …

Addressing the problem of two‐dimensional steady‐state thermal boundary recognition, a
hybrid algorithm of conjugate gradient method and social particle swarm optimization (CGM …

We consider an elliptic linear-quadratic parameter estimation problem with a finite number of
parameters. A novel a priori bound for the parameter error is proved and, based on this …

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 …

A shape identification scheme was developed to determine the geometric shape of the
inaccessible parts of two-dimensional objects using the measured temperatures on their …