A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O（H2）, which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.
This article proposes a diffused hepatitis B virus （HBV） model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.
This paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conductionconvection equations by using the lowest equal-order pairs of finite elements.This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition.The stability of the discrete scheme is derived under some regularity assumptions.Optimal error estimates are obtained by applying the standard Galerkin techniques.Finally,the numerical illustrations agree completely with the theoretical expectations.
