A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.

A Second Order Nonconforming Triangular Mixed Finite Element Scheme for the Stationary Navier-Stokes Equations

In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure. The convergence analysis is presented and optimal error estimates of both broken H^1-norm and L^2-norm for velocity as well as the L^2-norm for the pressure are derived.

STABILITY OF STATIONARY STATE SOLUTION FOR A REACTION DENSITY-DEPENDENT DIFFUSION EQUATION

In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u= 0 or u=1 is unstable under some assumptions, etc.

SOME LIOUVILLE-TYPE THEOREMS FOR THE STATIONARY 3D MAGNETO-MICROPOLAR FLUIDS

In this paper,we prove some Liouville-type theorems for the stationary magnetomicropolar fluids under suitable conditions in three space dimensions.We first prove that the solutions are trivial under the assumption of certain growth conditions for the mean oscillations of the potentials.And then we show similar results assuming that the solutions are contained in L^(p)(R^(3))with p∈[2,9/2).Finally,we show the same result for lower values of p∈[1,9/4)with the further assumption that the solutions vanish at infinity.

Parity-decomposition and moment analysis for stationary Wigner equation with inflow boundary conditions

We study the stationary Wigner equation on a bounded, one- dimensional spatial domain with inflow boundary conditions by using the parity decomposition of L. Barletti and P. F. Zweifel [Transport Theory Statist. Phys., 2001, 30（4-6）： 507-520]. The decomposition reduces the half-range, two-point boundary value problem into two decoupled initial value problems of the even part and the odd part. Without using a cutoff approximation around zero velocity, we prove that the initial value problem for the even part is well-posed. For the odd part, we prove the uniqueness of the solution in the odd L2-spaee by analyzing the moment system. An example is provided to show that how to use the analysis to obtain the solution of the stationary Wigner equation with inflow boundary conditions.

Existence of Solutions for Three Dimensional Stationary Incompressible Euler Equations with Nonvanishing Vorticity

In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable.

PENALTY-FACTOR-FREE STABILIZED NONCONFORMING FINITE ELEMENTS FOR SOLVING STATIONARY NAVIER-STOKES EQUATIONS

Two nonconforming penalty methods for the two-dimensional stationary Navier-Stokes equations are studied in this paper.These methods are based on the weakly continuous P1 vector fields and the locally divergence-free(LDF)finite elements,which respectively penalize local divergence and are discontinuous across edges.These methods have no penalty factors and avoid solving the saddle-point problems.The existence and uniqueness of the velocity solution are proved,and the optimal error estimates of the energy norms and L^(2)-norms are obtained.Moreover,we propose unified pressure recovery algorithms and prove the optimal error estimates of L^(2)-norm for pressure.We design a unified iterative method for numerical experiments to verify the correctness of the theoretical analysis.

On Partial Regularity of Suitable Weak Solutions to the Stationary Fractional Navier-Stokes Equations in Dimension Four and Five

In this paper, we investigate the partial regularity of suitable weak solutions to the multi- dimensional stationary Navier-Stokes equations with fractional power of the Laplacian （-△）^α （n/6 ≤α〈1 and a ≠ 1/2）. It is shown that the n ＋ 2 - 6α （3 ≤ n ≤5） dimensional Hausdorff measure of the set of the possible singular points of suitable weak solutions to the system is zero, which extends a recent result of Tang and Yu [19] to four and five dimension. Moreover, the pressure in ε-regularity criteria is an improvement of corresponding results in [1, 13, 18, 20].

Photodiode Circuit Macro-model for SPICE Si mulation

An accurate photodiode circuit macro-model is proposed for SPICE simulation. The definition and implementation of the macro-model is based on carrier stationary continuity equation. In this macro-model, the photodiode is a device of three pins, one for light intensity input and the other two for photocurrent output, which represent the relationship between photocurrent and incident light. The validity of the proposed macro-model is demonstrated with its PSPICE simulation result compared with reported experimental data.

Two-Level Stabilized Finite Volume Methods for the Stationary Navier-Stokes Equations

In this work,two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered.These methods are based on the local Gauss integration technique and the lowest equal-order finite element pair.Moreover,the two-level stabilized finite volume methods involve solving one small NavierStokes problem on a coarse mesh with mesh size H,a large general Stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size h=O(H^(2))or a large general Stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size h=O(|logh|^(1/2)H^(3)).These methods we studied provide an approximate solution(ue v h,pe v h)with the convergence rate of same order as the standard stabilized finite volume method,which involve solving one large nonlinear problem on a fine mesh with mesh size h.Hence,our methods can save a large amount of computational time.

Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schr¨odinger Equations with Unbounded Potentials and Nonlinearities

We propose a hierarchy of novel absorbing boundary conditions for the onedimensional stationary Schr¨odinger equation with general(linear and nonlinear)potential.The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schr¨odinger equations.It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition.Finally,we give the extension of these ABCs to N-dimensional stationary Schr¨odinger equations.

Recent Progress on Outflow/Inflow Problem for Viscous Multi-phase Flow

According to the boundary condition with the zero,negative,or positive velocity,the initial boundary problem for compressible multi-phase flow with the Dirichlet-type boundary condition can be classified into three cases:impermeable problem,inflow problem,or outflow problem.In this paper,we review the recent progress on the existence and nonlinear stability of the stationary solution to the outflow/inflow problems for viscous multi-phase flow.

Local Discontinuous Galerkin Methods for the 2D Simulation of Quantum Transport Phenomena on Quantum Directional Coupler

In this paper,we present local discontinuous Galerkin methods(LDG)to simulate an important application of the 2D stationary Schrödinger equation called quantum transport phenomena on a typical quantum directional coupler,which frequency change mainly reflects in y-direction.We present the minimal dissipation LDG(MD-LDG)method with polynomial basis functions for the 2D stationary Schrödinger equation which can describe quantum transport phenomena.We also give the MDLDG method with polynomial basis functions in x-direction and exponential basis functions in y-direction for the 2D stationary Schrödinger equation to reduce the computational cost.The numerical results are shown to demonstrate the accuracy and capability of these methods.