The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …

This paper reviews the state of the art and discusses recent developments in the field of
adaptive isogeometric analysis, with special focus on the mathematical theory. This includes …

We review different techniques to enforce essential boundary conditions, such as the
(nonhomogeneous) Dirichlet boundary condition, within a discrete variational framework …

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 …

This introductory chapter on the mathematical theory of finite element methods (FEMs)
discusses its h-version for elliptic boundary value problems in the displacement formulation …

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 revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert
spaces. Our key observation is that the general approach from [P. Heid and TP Wihler …

We prove that for compactly perturbed elliptic problems, where the corresponding bilinear
form satisfies a Gårding inequality, adaptive mesh-refinement is capable of overcoming the …

We introduce a simple initialization of the Maubach bisection routine for adaptive mesh
refinement which applies to any conforming initial triangulation. Using Maubach's routine …