DYNAMICS FOR VORTICES OF AN EVOLUTIONARY GINZBURG－LANDAU EQUATIONS IN 3 DIMENSIONS

91. Introduction\Nb consider thc fOllowing problemwhere Q = fl x I0, l], fl C R2 is a bounded smooth domaill, g f Z = afl x I0, l] - Sl is aC"-map such that deg(g,0O.) = d > 0 fOr all 0 5 = 5 l. Herc fl. = n x {z}. fi f Q --+ Ris a smooth function (sa}' C'(Q)) with positivc lowcr bound. ue t Q x R+ - R2.The aim of this article is to understand thc dynamics of vortices, or zeros, of solutionsu of (l.1)--(l.4). lts importance to the theory of superconductivity and applications areaddress…     

Stokes方程的稳定化间断有限元法

本文对定常的Stokes方程提出了一种新的间断有限元法,通过对通常的间断Galerkin有限元法应用稳定化思想,建立了一个相容的稳定间断有限元格式,对速度和压力的任意分片多项式空间Pl(K),Pm(K)的间断有限元逼近证明了解的存在唯一性,给出了关于速度和压力的L2 范数的最优误差估计．     

CONVERGENCE AND OPTIMALITY OF ADAPTIVE MIXED METHODS FOR POISSON'S EQUATION IN THE FEEC FRAMEWORK

Finite Element Exterior Calculus (FEEC) was developed by Arnold, Falk, Winther and others over the last decade to exploit the observation that mixed variational problems can be posed on a Hilbert complex, and Galerkin-type mixed methods can then be obtained by solving finite-dimensional subcomplex problems. Chen, Holst, and Xu (Math. Comp. 78 (2009) 35-53) established convergence and optimality of an adaptive mixed finite element method using Raviart-Thomas or Brezzi-Douglas-Marini elements for Poisson's equation on contractible domains in $\mathbb{R}^2$, which can be viewed as a boundary problem on the de Rham complex. Recently Demlow and Hirani (Found. Math. Comput. 14 (2014) 1337-1371) developed fundamental tools for a posteriori analysis on the de Rham complex. In this paper, we use tools in FEEC to construct convergence and complexity results on domains with general topology and spatial dimension. In particular, we construct a reliable and efficient error estimator and a sharper quasi-orthogonality result using a novel technique. Without marking for data oscillation, our adaptive method is a contraction with respect to a total error incorporating the error estimator and data oscillation.     

STABILITY ANALYSIS OF FINITE ELEMENT METHODS FOR THE ACOUSTIC WAVE EQUATION WITH ABSORBINGBOUNDARY CONDITIONS (PART I)

1.IntroductionInthenumericalsimulationofwavepropagationinunboundedorsemi-unboundedmediumitisnecessarytointroduceartificialboundariestoobtainfinitecomputational'regions.Thensomeboundaryconditionshavetobeimposedontheseboundaries,whichshouldeliminatethe...     

THE GLOBAL ARTIFICIAL BOUNDARY CONDITIONS FOR NUMERICAL SIMULATIONS OF THE 3D FLOW AROUND A SUBMERGED BODY

We consider the numerical approximations of the three-dimensional steady potential flow around a body moving in a liquid of finite constant depth at constant speed and distance below a free surface in a channel. One vertical side is introduced as the up-stream artificial boundary and two vertical sides are introduced as the downstream arti-ficial boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the original problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. After solving the variational problem by the finite element method, we obtain the numerical approximation of the original problem. The numerical examples show that the artificial boundary conditions given in this paper are very effective.     

RECENT ADVANCES OF UPSCALING METHODS FOR THE SIMULATION OF FLOW TRANSPORT THROUGH HETEROGENEOUS POROUS MEDIA

We review some of our recent efforts in developing upscaling methods for simulatingthe flow transport through heterogeneous porous media. In particular, the steady flowtransport through highly heterogeneous porous media driven by extraction wells and theflow transport through unsaturated porous media will be considered.     

两同心旋转球间流动问题分歧解的连续算法

1引言本文数值地考察了两个同心旋转球之间的定常轴对称不可压流动．这种流动被称为球面Couette流（SphericalCouetteFlow）,简称SCF．SCF对干天体物理,地球物理和工程应用均具重要意义,虽然过往所做的研究甚少（一方面由于分析研究的难度,另方面,所做的实验也少）,目前,对其研究的兴趣有增长的趋势．实验发现,SCF在低雷诺数下既是轴对称的,又是关于赤道成反射对称的（Khlebutin［‘］,ZlereP＆SawatskiL‘）．ZiereP＆Sawatski和Wimmer［’］都发现SCF有临界雷诺数Rec,当Re＞Rec,有泰勒旋涡（TaylorVortices）形成…     

STABLE FOURTH-ORDER STREAM-FUNCTION METHODS FOR INCOMPRESSIBLE FLOWS WITH BOUNDARIES

Fourth-order stream-function methods are proposed for the time dependent, incom- pressible Navier-Stokes and Boussinesq equations. Wide difference stencils are used instead of compact ones and the boundary terms are handled by extrapolating the stream-function values inside the computational domain to grid points outside, up to fourth-order in the noslip condition. Formal error analysis is done for a simple model problem, showing that this extrapolation introduces numerical boundary layers at fifth-order in the stream-function. The fourth-order convergence in velocity of the proposed method for the full problem is shown numerically.     

IMPLICIT-EXPLICIT MULTISTEP FINITE ELEMENT-MIXED FINITE ELEMENT METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

The transient behavior of a semiconductor device consists of a Poisson equa-tion for the electric potential and of two nonlinear parabolic equations for the electrondensity and hole density.The electric potential equation is discretized by a mixed finiteelement method. The electron and hole density equations are treated by implicit-explicitmultistep finite element methods. The schemes are very efficient. The optimal order errorestimates both in time and space are derived.     

非饱和土壤水流问题的广义差分法及其数值模拟

本文利用广义差分法建立了一维非饱和水流问题的守恒形式的数值模型,讨论了半离散广义差分解和全离散广义差分解的存在唯一性,并给出了其误差估计．数值结果表明,该格式具有计算量小和稳定性等特点,且对求解非饱和水流问题有较好的适应性．     

非饱和水流问题的混合元法及其数值模拟

1.引 言 均质土壤中的地下水流动可归结为非饱和土壤水的流动,是土壤水未完全充满孔隙时的流动,是多孔介质流体运动的一种重要形式.非饱和流动的预报在大气科学、土壤学、农业