We consider nonlinear algebraic systems resulting from numerical discretizations of
nonlinear partial differential equations of diffusion type. To solve these systems, some …

This article is a review of basic concepts and tools devoted to a posteriori error estimation for
problems solved with the finite element method. For the sake of simplicity and clarity, we …

For linear problems, domain decomposition methods can be used directly as iterative
solvers but also as preconditioners for Krylov methods. In practice, Krylov acceleration is …

We study in this paper a posteriori error estimates for H 1-conforming numerical
approximations of diffusion problems with a diffusion coefficient piecewise constant on the …

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 …

Tucker decomposition can provide an intuitive summary to understand brain function by
decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and …

We consider nonsmooth partial differential equations associated with a minimization of an
energy functional. We adaptively regularize the nonsmooth nonlinearity so as to be able to …

Two research subjects in geosciences which lately underwent significant progress are
treated in this review. In the first part, we focus on one key ingredient for the numerical …

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 …

This paper develops a general abstract framework for a posteriori estimates for immiscible
incompressible two-phase flows in porous media. We measure the error by the dual norm of …