Finite element and finite difference methods have been widely used, among other methods, to numerically solve the Fokker-Planck equation for investigating the time history of the probability density function of linear and nonlinear 2d and 3d problems, and also the application to 4d problems has been addressed. However, due to the enormous increase of the computational costs, different strategie...

The paper presents a Galerkin approach for the solution of nonlinear beam equations. The approach is energy consistent, i.e., it is shown that the weighted residual integral describes energy flow. The Galerkin approach gives accurate results with less degrees of freedom as compared to low-order finite element formulation. The Galerkin approach also leads to a nonlinear order-reduction technique...

‖f(u)− f(v)‖−1 ≤ L‖u− v‖−1. We drop the dependence of f on x to emphasis the nonlinearity in u. Let Vh ⊂ H 0 (Ω) be the linear finite element space associated to a quasi-uniform mesh Th. The nonlinear Garlerkin method is: find uh ∈ Vh such that (2) Auh = f(uh) in Vh, where A : H 0 (Ω)→ H−1(Ω) is the elliptic operator defined by −∆. We shall assume the existence and locally uniqueness of the sol...

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic PDE on two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The twomeshes beingmutually independent on the overlap region, a triangle belonging to one triangul...

in this study, focuses on applying the hp-version for forward modeling. the eit forward solver is normally based on the conventional finite element method (hfem). in h-fem, the polynomial order p of the element shape functions is constant and the element size h, is decreased. to accurately simulate the forward solution with the hfem, a mesh with large number of nodes and elements is usually need...

In this paper, we use finite element methods to simulate the hydrodynamical systems governing the motions of nematic liquid crystals in a bounded domain Ω. We reformulate the original model in the weak form which is consistent with the continuous dissipative energy law for the flow and director fields in W(Ω) (σ > 0 is an arbitrarily small number). This enables us to use convenient conformal C0...

using the highly recommended numerical techniques, a finite element computer code is developed to analyse the steady incompressible, laminar and turbulent flows in 2-d domains with complex geometry. the petrov-galerkin finite element formulation is adopted to avoid numerical oscillations. turbulence is modeled using the two equation k-ω model. the discretized equations are written in the form o...

An adaptive finite difference method for first order nonlinear systems of ordinary differential equations subject to multipoint nonlinear boundary conditions is presented. The method is based on a discretization studied earlier by H. B. Keller. Variable order is provided through deferred corrections, while a built-in natural asymptotic estimator is used to automatically refine the mesh in order...

condition monitoring of bldc motors due to their important applications is gaining more and more significance. rotor eccentricity is one of the most important sources of faults in these motors. up to now, detection methods of this fault under nonstationary conditions are limited to complicated and time-consuming methods using wavelets and cohen class algorithms which are difficult to implement ...