We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of Kozlov, Maz′ya and Fomin (1991) applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The num...

We study finite element methods for semilinear stochastic partial differential equations. Error estimates are established. Numerical examples are also presented to examine our theoretical results. Mathematics Subject Classification (2000) 65N30 · 65N15 · 65C30 · 60H15

Analysis of pre onditioners for saddle-point problems D. Loghin and A. J. Wathen Mixed nite element formulations give rise to large, sparse, blo k linear systems of equations the solution of whi h is often sought via a pre onditioned iterative te hnique. In this work we present a general analysis of blo kpre onditioners based on the stability onditions inherited from the formulation of the nite...

Due to existence of uncertainties in input geometrical properties of fractures, there is not any unique solution for assessing the stability of slopes in jointed rock masses. Therefore, the necessity of applying probabilistic analysis in these cases is inevitable. In this study a probabilistic analysis procedure together with relevant algorithms are developed using Discrete Fracture Network-Dis...

Herein, a theoretical study on the stability of some vic-dioxime complexes of Ni(II), Pd(II) and Pt(II) in gas and aqueous phases is reported. The DFT/M06/SDD and DFT/M06/6-31G+(d,p) levels of theory were adopted for the metal ions and for every other element respectively. Structural analyses of investigated complexes have revealed square planar geometries stabilized by two O–H⋯Cl hydrogen bond...