This special issue of Computational Methods in Applied Mathematics is dedicated to
Thomas Apel on the occasion of his 60th birthday in 2022. He was and is a leading figure in …

We analyze the convergence rate of a multilevel quasi-Monte Carlo (MLQMC) Finite
Element Method (FEM) for a scalar diffusion equation with log-Gaussian, isotropic …

This paper is concerned with approximations and related discretization error estimates for
the normal derivatives of solutions of linear elliptic partial differential equations. In order to …

We present an extension of the convergence analysis for Richardson-extrapolated
polynomial lattice rules from [J. Dick, T. Goda, and T. Yoshiki, SIAM J. Numer. Anal., 57 …

This article deals with error estimates for the finite element approximation of Neumann
boundary control problems in polyhedral domains. Special emphasis is put on singularities …

We present an extension of the convergence analysis for Richardson-extrapolated
polynomial lattice rules from [Josef Dick, Takashi Goda and Takehito Yoshiki: Richardson …

We investigate the use of a class of quasi-Monte Carlo (QMC) quadrature rules, called
Extrapolated Polynomial Lattices, to approximate expected values of quantities of interest …

In this paper, we study a finite element method overcoming corner singularities for elliptic
optimal control problem posed on a polygon. Based on a corner singularity decomposition of …

Partial differential equations (PDEs) with incomplete knowledge on differential operators
arise in science and engineering. This lack of knowledge results in uncertainty in the …

We derive a residual based a posteriori error estimate for the outer normal flux of
approximations to the diffusion problem with variable coefficient. By analyzing the solution of …