A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal approximation. This explicit time integrator allows for mean-square error bounds independent of the space discretisation and thus do not suffer from a step si...

We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the torques and forces derive from a potential energy, and thus the global equation is an Hamiltonian dynamics. The use of an explicit symplectic time integration sche...

Abstract. A fully discrete approximation of the linear stochastic wave equation driven by additive noise is presented. A standard finite element method is used for the spatial discretisation and a stochastic trigonometric scheme for the temporal approximation. This explicit time integrator allows for error bounds independent of the space discretisation and thus do not have a step size restricti...

discrete element method (dem) is extensively used for mathematical modeling and simulating the behavior of discrete discs and discrete spheres in two and three dimensional space, respectively. prediction of particles flow regime, power draw and kinetic energy for a laboratory or an industrial mill is possible by dem simulation. in this article, a new approach was used to assess the main paramet...

We study the linearization of three dimensional Regge calculus around Euclidean metric. We provide an explicit formula for the corresponding quadratic form and relate it to the curlt curl operator which appears in the quadratic part of the Einstein-Hilbert action and also in the linear elasticity complex. We insert Regge metrics in a discrete version of this complex, equipped with densily defin...

Two phase flow problem in a porous medium is governed by a system of nonlinear equations. One is an elliptic equation for the pressure and the other is a parabolic equation for the concentration of one of the fluids. Since the pressure appears in the concentration only through its velocity field, we choose a mixed finite element to approximate the pressure equation and use the standard Galerkin...

In this paper we study inverting random functions under the maximum likelihood estimation (MLE) criterion in the discrete setting. In particular, we consider how many independent evaluations of the random function at a particular element of the domain are needed for reliable reconstruction of that element. We provide explicit upper and lower bounds for MLE, both in the nonparametric and paramet...

Tube Hydroforming (THF) is getting an increasing amount of attention in industry. THF has advantages such as weight reduction, high dimensional accuracy, and high rigidity. However, this forming process requires precise control of internal pressure and axial feeding. Additionally, in most cases prebending processes must be performed on the tubes before the hydroforming process can be carried ou...

By using an efficient partial order and concept of gH-differentiability oninterval-valued functions, we investigate some new variants of Gronwall typeinequalities on time scales, which provide explicit bounds on unknownfunctions. Our results not only unify and extend some continuousinequalities, but also in discrete case, all are new.