Abstract This paper addresses two sampling methodologies to respectively estimate the Owen value and Banzhaf–Owen for TU-games with a priori unions. Both proposals are based on stratified set of those coalitions that compatible system unions according their cardinalities. These analysed in terms theoretical properties establishment bounds absolute error from statistical point view. Finally, we ...

In this paper we analyze the coupling of local discontinuous Galerkin (LDG) and boundary element methods as applied to linear exterior boundary value problems in the plane. As a model problem we consider a Poisson equation in an annular polygonal domain coupled with a Laplace equation in the surrounding unbounded exterior region. The technique resembles the usual coupling of finite elements and...

In this thesis we study so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of quasilinear partial differential equations. The two-grid method is constructed by first solving the nonlinear system of equations stemming from the discontinuous Galerkin finite element method on a coarse mesh partition; then, this coarse solution is used to linearis...

In this second part of the series, we focus on approximating the Hele-Shaw problem via the Cahn-Hilliard equation ut + ∆(ε∆u − εf(u)) = 0 as ε ↘ 0. The primary goal of this paper is to establish the convergence of the solution of the fully discrete mixed finite element scheme proposed in [21] to the solution of the Hele-Shaw (Mullins-Sekerka) problem, provided that the HeleShaw (Mullins-Sekerka...