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 …

Structural analysis is an essential tool for design engineers. Mesh generation is the basic
step in any simulation. In practice of finite-element stress analysis, the engineer first needs to …

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 consider adaptive finite element methods for second-order elliptic PDEs, where the
arising discrete systems are not solved exactly. For contractive iterative solvers, we …

We consider scalar semilinear elliptic PDEs where the nonlinearity is strongly monotone, but
only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite element …

The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to
compute an approximation of user-prescribed accuracy at quasi-minimal computation time …

We consider a second-order elliptic boundary value problem with strongly monotone and
Lipschitz-continuous nonlinearity. We design and study its adaptive numerical …

We prove convergence with optimal algebraic rates for an adaptive finite element method for
nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also …

We consider an adaptive algorithm for finite element methods for the isogeometric analysis
(IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in …

We consider a general nonsymmetric second-order linear elliptic partial differential equation
in the framework of the Lax–Milgram lemma. We formulate and analyze an adaptive finite …