An extension of the deterministic variational multiscale (VMS) approach with algebraic subgrid scale (SGS) modeling is considered for developing stabilized finite element formulations for the stochastic advection and the incompressible stochastic Navier-Stokes equations. The stabilized formulations are numerically implemented using the spectral stochastic formulation of the finite element metho...

Abstract. An efficient method for obtaining numerical solutions of a stochastic variational inequality modeling an elasto-plastic oscillator with noise is considered. Since Monte Carlo simulations for the underlying stochastic process are too slow to produce results, as an alternative, approximate solutions of the partial differential equation defining the invariant measure of the process are s...

Computer simulations are an indispensable tool in microfluidics because of the lack of analytical solutions. We have developed a simulation tool in Matlab based on the finite element method (FEM). At the present stage, the tool can be employed to handle general second order partial differential equations in two dimensions. The tool has been applied to model incompressible laminar flow, and it h...

The accuracy of the Extended Finite Element Method (XFEM) in solving problems of straining plate with central crack is analyzed. Numerical solutions for displacements and stresses are compared with analytical solutions, while numerical solutions for stress intensity factor are compared with empirical solutions. The impact of the mesh density and near tip (NT) enrichment function are investigate...

finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.

The boundary layer flow of Cu-water based nanofluid with heat transfer over a stretching sheet is numerically studied. Second order velocity slip flow model is considered instead of no-slip at the boundary. The governing partial differential equations are transformed into ordinary one using similarity transformation, before being solved numerically. Numerical solutions of these equations are ob...

Interface cracks are seldom subjected to pure Mode I or pure Mode II conditions. Station~y interface cracks between two distinct, bonded elastic-creep materials subjected to remotely applied mixed mode loading are simulated. The finite element method (FEM) is used to examine crack tip fields and candidate driving force parameters for crack growth. Plane strain conditions are assumed. In most ca...

Skeletal injury operations are in general of high complexity and require extreme accuracy. That is why it seems practical that prior to a surgical intervention a geometric and mechanic model is prepared, which can be used to simulate various operational solutions. We present here a computerized system, which we call MedEdit, that helps the surgeon to plan the operation and with the use of a Fin...

To study electromagnetic scattering from dielectric rough surfaces, a hybrid finite element method (FEM) combined with boundary integral equations (BIE) is extended to the scattering problem with two half-open regions. Integral boundaries, as truncated boundaries of the FEM region, are employed as artificial boundaries of dielectric rough surfaces above and below the rough surface. In the hybri...

In this paper, the C-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Keywords—Nonlinear fourth-ord...