When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

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 mainly devoted to a review on fast BEMs for elastodynamics, with particular
attention on time-harmonic fast multipole methods (FMMs). It also includes original results …

Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …

Our times can be characterized by, among many other attributes, the seemingly increasing
speed of everything. Within science, it has led to the publication explosion, which reflects the …

We derive a posteriori error estimates for a class of second-order monotone quasi-linear
diffusion-type problems approximated by piecewise affine, continuous finite elements. Our …

The importance of accuracy verification methods was understood at the very beginning of
the development of numerical analysis. Recent decades have seen a rapid growth of results …

A residual-based a posteriori error estimate for the Poisson problem with discontinuous
diffusivity coefficient is derived in the case of a virtual element discretization. The error is …

The paper proposes a parallel algorithm for solving large overdetermined systems of linear
algebraic equations with a dense matrix. This algorithm is based on the use of a modification …

In this paper we develop adaptive iterative coupling schemes for the Biot system modeling
coupled poromechanics problems. We particularly consider the space–time formulation of …