This paper presents a exible approach to domain decomposition preconditioning for problems expressed in terms of local stiiness matrices of subdomains. Evaluation of the preconditioner requires fully parallelizable local computations and the solution of a global auxiliary problem with few variables per subdomain. Convergence factors can be bounded using properties of the local stiiness matrices...

In this paper, we present a theory for bounding the minimum eigenvalues, maximum eigenvalues, and condition numbers of stiffness matrices arising from the p-version of finite element analysis. Bounds are derived for the eigenvalues and the condition numbers, which are valid for stiffness matrices based on a set of general basis functions that can be used in the p-version. For a set of hierarchi...

— Many problems in continuüm mechanics involve an incompressibility condition, usually in the form of a divergence constraint. The numerical discretization of such a constraint présents some interesting problems with regard to stabïlity. In this paper we analyze certain stability properties, typical of high degree, conforming finite element approximations for problems with a divergence constrai...

This paper gives a precise description of regularities of solutions and their derivatives of all orders for elliptic problems on polyhedral domains in the frame of the countably normed spaces with weighted Ck-norms in neighborhoods of vertices, edges and vertex-edges. Under the guidance of the regularity theory, the geometric meshes and P-Q distribution (bilinear-linear or linear-uniform) of el...

— The approximation of solutions of elliptic problems of order 2 î over twodimensional polygonal domains by the p-version of the finite element method is investigated. Optimal rates of convergence are established for the case when éléments possessing C ~ continuity are used. Résumé. — L'approximation des solutions de problèmes elliptiques d'ordre 2 î dans un domaine à deux dimensions est traité...

A new variational (dis)continuous Galerkin finite element method is presented for linear free surface gravity water wave equations. In this method, the space-time finite element discretization is based on a discrete variational formulation analogous to a version of Luke’s variational principle. The finite element discretization results into a linear algebraic system of equations with a symmetri...

Only very recently, Sayas [The validity of Johnson-Nédélec's BEM-FEM coupling on polygonal interfaces. SIAM J Numer Anal 2009;47:3451-63] proved that the Johnson-Nédélec one-equation approach from [On the coupling of boundary integral and finite element methods. Math Comput 1980;35:1063-79] provides a stable coupling of finite element method (FEM) and boundary element method (BEM). In our work,...

introduction: with the rapid increase in use of lasers in medical treatments, it is important to understand the mechanisms of heat transfer in biological tissues in order to minimize damage to the tissues resulting from extra heat applied. the aim of this study is to investigate the temperature distribution in living biological tissues when laser irradiation is used in a treatment. methods:  in...

objective: intrusion as a type of tooth movement is managed by different mechanotherapies during various treatment stages. the morphology of the apical third of the teeth to be intruded plays an important role in the risk of root resorption due to the raise of stresses. the main goal of this study was to compare various types of apical third of the teeth while loaded by an intrusive force. mate...