The performance of an 8-noded hexahedron C1* element in elasticity is investigated. Three translational displacements and their derivatives as strain in each direction are considered as degrees of freedom (d.o.f.’s) at each node. The geometric mapping is enforced using a C0 element with no derivative as nodal d.o.f.’s . The stiffness matrix of the element is also computed using a transformation...

We present a new method [7] for numerically solving elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. We use a relaxed iterative method which consists in calculating successive corrections to the solution in patches of finite elements. We analyse the spectral properties of the iteration operator [6]. We show how to evaluate the best relaxation parame...

The aim of this paper is to present a new class of finite elements on quadrilaterals where the approximation is polynomial on each element K. In the case of Lagrange finite elements, the degrees of freedom are the values at the vertices and in the case of mixed finite elements the degrees of freedom are the mean values of the fluxes on each side. The degres of freedom are the same as those of c...

We present a new discretization method for homogeneous convectiondiffusion-reaction boundary value problems in 3D that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements. The element stiffness matrices are constructed by means of local boundary element techniques. Our method, which we refer to as a BEM-based FEM, can therefore be considered a local ...

several appliances have been used for palatal expansion for treatment of posterior cross bite. the purpose of this study was to evaluate the stress induced in the apical and crestal alveolar bone and the pattern of tooth displacement following expansion via removable expansion plates or fixed-banded palatal expander using the finite element method (fem) analysis.two 3d fem models were designed ...

Mortar finite element methods allow for a flexible and efficient coupling of arbitrary nonconforming interface meshes and are by now quite well established in nonlinear contact analysis. In this paper, a mortar method for three-dimensional (3D) finite deformation contact is presented. Our formulation is based on so-called dual Lagrange multipliers, which in contrast to the standard mortar appro...

We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics. The solution of these equations requires solving multiple leng...

The presented article contains a 3D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes of a prescribed volume V0 of elements. The finite volume meshes are used with the Finite Element approach. The FEM analysis enables to deal with a set of coupled nonlinear differential equations that describes the electrodiffusional problem. Mesh quality a...

In this paper we present parallel 2D and 3D finite element computation of unsteady, incompressible free-surface flows. The computations are based on the DeformableSpatial-Domain/Stabilized Space-Time (DSD/SST) finite element formulation, which takes automatically into account the motion of the free surface. The free-surface height is governed by a kinematic free-surface condition, which is also...