This monograph is centered on mathematical modeling, innovative numerical algorithms
and adaptive concepts to deal with fracture phenomena in multiphysics. State-of-the-art …

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 …

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 …

There is increasing interest in the material point method (MPM) as a means of modelling
solid mechanics problems in which very large deformations occur, eg in the study of …

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

The expansion of modern computing power has seen a commensurate rise in the reliance
on numerical simulations for engineering and scientific purposes. Output error estimation …

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