Compared with standard Galerkin finite element methods, mixed methods for second-order elliptic problems give readily available flux approximation, but in general at the expense of having to deal with a more complicated discrete system. This is especially true when conforming elements are involved. Hence it is advantageous to consider a direct method when finding fluxes is just a small part of ...

1 P. YU ET AL. KB AND GALERKIN METHODS 2 SUMMARY The objective of this paper is to consider the dynamic motions of second order, weakly nonlinear, discrete systems. The main attention is focused on a comparison, for such systems, of the method of Krylov-Bogoliubov (KB) and an enhanced Galerkin (EG) method which produce seemingly diierent solutions. Despite the apparent diierences, the two metho...

in this paper, the ritz-galerkin method in bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (mhd) flow of third grade fluid between the two plates. the properties of the bernstein  polynomials together with the ritz-galerkin method are used to reduce the solution of the mhd couette flow of non-newtonian fluid in a porous medium to the solution o...

The optimal rate of convergence of the wave equation in both the energy and the L-norms using continuous Galerkin method is well known. We exploit this technique and design a fully discrete scheme consisting of coupling the nonstandard finite difference method in the time and the continuous Galerkin method in the space variables. We show that, for sufficiently smooth solution, the maximal error...

A discontinuous Galerkin finite element heterogeneous multiscale method is proposed for advectiondiffusion problems with highly oscillatory coefficients. The method is based on a coupling of a discontinuous Galerkin discretization for an effective advection-diffusion problem on a macroscopic mesh, whose a priori unknown data are recovered from micro finite element calculations on sampling domai...

Abstract We prove existence results for a reaction-diffusion system modeling the spread of early tumors. The existence result is proved by the Faedo-Galerkin method, a priori estimates and the compactness method. Moreover, we construct a finite volume scheme to our model, we establish existence of discrete solutions to this scheme, and show that it converges to a weak solution. Finally, some nu...

This article devises a new primal-dual weak Galerkin finite element method for the convection-diffusion equation. Optimal order error estimates are established approximations in various discrete norms and standard L2 norms. A series of numerical experiments conducted reported to verify theoretical findings.

Abstract. In this paper, we consider anisotropic diffusion with decay, which takes the form α(x)c(x) − div[D(x)grad[c(x)]] = f(x) with decay coefficient α(x) ≥ 0, and diffusivity coefficient D(x) to be a second-order symmetric and positive definite tensor. It is well-known that this particular equation is a second-order elliptic equation, and satisfies a maximum principle under certain regulari...

We present a general result of approximate controllability for the bilinear Schrödinger equation (with wave function varying in the unit sphere of an infinite dimensional Hilbert space), under the hypothesis that the Schrödinger operator has discrete spectrum and that the control potential couples all eigenstates. The control method is based on a tracking procedure for the Galerkin approximatio...

An efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation the Legendre orthogonal polynomials, while time derivative discretized by using symmetric Euler finite difference schema. stability convergence of ...