the main goal of this study was to evaluate differences in stress distribution relevant to the number of implants under an anterior bridge when combined with a removable partial denture in the posterior region.four three-dimensional finite element models (3d fem) were designed from a mandible containing an implant-supported bridge extending between canines, and a bilateral distal extension remo...

We will overview a series of recent works [1, 2, 3, 4, 5, 6, 7] all related to some multiscale problems motivated by practical problems in Mechanics. The common denominator of all these works is that they address multiscale problems where the geometry of the microstructures is not periodic. Random modelling, but not only (see e.g. [2, 3]), can then be used in order to account for the imperfecti...

A new numerical scheme based on the H-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one spa...

A general framework for weak residual error estimators applying to various types of boundary value problems in connection with finite element and finite volume approximations is developed. Basic ideas commonly shared by various applications in error estimation and adaptive computation are presented and illustrated. Some numerical results are given to show the effectiveness and efficiency of the...

Practical engineering problems in heat transfer and fluid flow involve one or more governing equations, together with some boundary conditions over a domain. The domain is often complex and non-uniform. The ability to use a mesh of finite elements to accurately discretise domain of any size and shape makes the finite element method a powerful tool to numerically analyse problems in these areas....

A two-dimensional (2-D) explicit dynamics finite element (FE) model of a rolling element bearing was solved using a commercial FE software package, LS-DYNA. It was found that the modelled bearing vibration signals contain a significant amount of numerical noise. This paper provides an explanation of the physical mechanism by which the numerical noise is generated. The noise frequencies were ana...

In this paper, a novel method for incorporating automatic, patient-specific, structural analysis in computer-aided preoperative planning is described. Special emphasis has been placed on accurately capturing the mechanical behavior of the implant-to-bone interface where failure may occur. A finite element solver was developed and integrated into our computer-aided planning system for implant de...

Expanded mixed finite element method is introduced to approximate the two-dimensional Sobolev equation. This formulation expands the standard mixed formulation in the sense that three unknown variables are explicitly treated. Existence and uniqueness of the numerical solution are demonstrated. Optimal order error estimates for both the scalar and two vector functions are established.

A new finite element method is proposed for the numerical solution of a class of initial-boundary value problems for first-order hyperbolic systems in one space dimension. An application of our procedure to a system modeling gas flow in a pipe is discussed. Asymptotic error estimates are derived in the L norm in space.

The finite element method is well suited to the numerical solution of the partial differential equations arising in finance because they allow for a posteriori error estimates and mesh adaptivity. The method will be described on three simple examples and its advantages will be emphasized.