In this paper, we prove existence results for a Predator-prey system in a polluted environment. The existence result is proved by the Schauder fixed-point theorem. Moreover, we construct a combined finite volume finite element scheme to our model, we establish existence of discrete solutions to this scheme, and show that it converges to a weak solution. The convergence proof is based on derivin...

In this article, we present a finite element variational multiscale (VMS) method for incompressible flows based on two local Gauss integrations, and compare it with common VMS method which is defined by a low order finite element space Lh on the same grid as Xh for the velocity deformation tensor and a stabilization parameter a. The best algorithmic feature of our method is using two local Gaus...

The Moving Finite Element method for the solution of time-dependent partial dierential equations is a numerical solution scheme which allows the automatic adaption of the nite element approximation space with time. An analysis of how this method models the steady solutions of a general class of parabolic linear source equations is presented. It is shown that the steady solutions of the Moving F...

The Moving Finite Element method for the solution of time-dependent partial diierential equations is a numerical solution scheme which allows the automatic adaption of the nite element approximation space with time. An analysis of how this method models the steady solutions of a general class of parabolic linear source equations is presented. It is shown that under certain conditions the steady...

the paper investigates into the vibrational characteristics of the truck chassis including the natural frequencies and mode shapes. truck chassis forms the structural backbone of a commercial vehicle. when the truck travels along the road, the truck chassis is excited by dynamic forces caused by the road roughness, engine, transmission and more. modal analysis using finite element method (fem) ...

We describe multiscale mortar mixed finite element discretizations for second order elliptic and nonlinear parabolic equations modeling Darcy flow in porous media. The continuity of flux is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. We discuss the construction of multiscale mo...

In this article we define an Eulerian level set method for a partial differential equation on an evolving hypersurface Γ (t) contained in a domain Ω ⊂ R. The key idea is based on formulating the partial differential equations on all level set surfaces of a prescribed time dependent function Φ whose zero level set is Γ (t). The resulting equation is then solved in one dimension higher but can be...

modelling of crack propagation by finite element method under mixed mode conditions is of prime importance in fracture mechanics. this paper describes an application of finite element method to the analysis of mixed mode crack growth in linear elastic fracture mechanics. crack growth process is simulated by an incremental crack-extension analysis based on the maximum principal stress criterion,...

In this article we consider the approximation of singularly perturbed boundary value problems using a local adaptive grid h-refinement for finite element method, the variation iteration method and the homotopy perturbation method. The solution to such problems contains boundary layers which overlap and interact and the numerical approximation must take this into account in order for the resulti...

In this thesis we study so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of quasilinear partial differential equations. The two-grid method is constructed by first solving the nonlinear system of equations stemming from the discontinuous Galerkin finite element method on a coarse mesh partition; then, this coarse solution is used to linearis...