In the variational formulation of finite element models for mechanics problems, boundary conditions are classified as either essential or natural. The traction boundary conditions are identified as natural in many commonly-used finite element models. A valid finite element mode must satisfy explicitly the essential boundary conditions, since the latter are satisfied implicitly as a posteriori c...

This paper discusses the modeling of unsteady-state mass diffusion under concentrationdependent diffusivity through an orthotropic medium. Historically, a simpler one-dimensional formulation with constant medium properties has been used, leading to approximate solutions. The present work uses a finite element formulation with finite difference discretization in time. The code includes an elemen...

This paper deals with the numerical computation of the structural and acoustic response of a building to an incoming wave field generated by high-speed surface railway traffic. The source model consists of a moving vehicle on a longitudinally invariant track, coupled to a layered ground modelled with a boundary element formulation. The receiver model is based on a substructuring formulation and...

In this article, an adaptive least-squares mixed finite element method is studied for pseudo-parabolic integro-differential equations. The solutions of least-squares mixed weak formulation and mixed finite element are proved. A posteriori error estimator is constructed based on the least-squares functional and the posteriori errors are obtained. Keywords—Pseudo-parabolic integro-differential eq...

A recently developed Eulerian finite element method is applied to solve advectiondiffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, finite element methods tend to be unstable unless the mesh is sufficiently fine. The paper introduces a stabilized finite element formulation based on the SUPG technique. An error analysis of the method is giv...

We consider a finite element method based on biorthogonal or quasi-biorthogonal systems for the biharmonic problem. The method is based on the primal mixed finite element method due to Ciarlet and Raviart for the biharmonic equation. Using different finite element spaces for the stream function and vorticity, this approach leads to a formulation only based on the stream function. We prove optim...

We propose a mixed formulation for non-isothermal Oldroyd–Stokes problem where the both extra stress and the heat flux’s vector are considered. Based on such a formulation, a dual mixed finite element is constructed and analyzed. This finite element method enables us to obtain precise approximations of the dual variable which are, for the non-isothermal fluid flow problems, the viscous and poly...

This paper presents three formulations combining domain decomposition based finite element method with linear preconditioned conjugate gradient (LPCG) technique for solving large-scale problems in structural mechanics on parallel processing machines. In the first formulation called the Global Interface Formulation (GIF), the PCG algorithm is applied on the assembled interface stiffness coeffici...