共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper establishes a new finite volume element scheme for Poisson equation on triangular meshes. The trial function space
is taken as Lagrangian cubic finite element space on triangular partition, and the test function space is defined as piecewise
constant space on dual partition. Under some weak condition about the triangular meshes, the authors prove that the stiffness
matrix is uniformly positive definite and convergence rate to be O(h
3) in H
1-norm. Some numerical experiments confirm the theoretical considerations. 相似文献
2.
<正> Seawater intrusion problem is considered in this paper.Its mathematical model is anonlinear coupled system of partial differential equations with initial boundary problem.It consistsof the water head equation and the salt concentration equation.A combined method is developedto approximate the water head equation by mixed finite element method and concentration equationby discontinuous Galerkin method.The scheme is continuous in time and optimal order estimates inH~1-norm and L~2-norm are derived for the errors. 相似文献
3.
<正> A nonconforming finite element method for the nonlinear parabolic equations is studied inthis paper.The convergence analysis is presented and the optimal error estimate in L~2(‖·‖_h)norm isobtained through Ritz projection technique,where ‖·‖_h is a norm over the finite element space. 相似文献
4.
This paper investigates L~∞-estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods.The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions.The authors derive L~∞-estimates for the mixed finite element approximation of nonlinear optimal control problems.Finally,the numerical examples are given. 相似文献
5.
This paper proposes the least-squares Galerkin finite element scheme to solve second-order hyperbolic equations. The convergence
analysis shows that the method yields the approximate solutions with optimal accuracy in (L
2(Ω))2 × L
2(Ω) norms. Moreover, the method gets the approximate solutions with second-order accuracy in time increment. A numerical example
testifies the efficiency of the novel scheme. 相似文献
6.
For a general second-order variable coefficient elliptic boundary value problem in three dimensions,the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements.In addition,the estimate for the W1,1 -seminorm of the discrete derivative Green’s function is given.Finally,the authors show that the derivatives of the finite element solution uh and the corresponding interpolantΠu are superclose in the pointwise sense of the L∞-norm. 相似文献
7.
Min Yang 《系统科学与复杂性》2008,21(1):129-143
The author considers a thermal convection problem with infinite Prandtl number in two or three dimensions. The mathematical model of such problem is described as an initial boundary value problem made up of three partial differential equations. One equation of the convection-dominated diffusion type for the temperature, and another two of the Stokes type for the normalized velocity and pressure. The approximate solution is obtained by a penalty finite volume method for the Stokes equation and a multistep upwind finite volume method for the convection-diffusion equation. Under suitable smoothness of the exact solution, error estimates in some discrete norms are derived. 相似文献
8.
9.
In this paper, a new triangular element (Quasi-Carey element) is constructed by the idea of Specht element. It is shown that this Quasi-Carey element possesses a very special property, i.e., the consistency error is of order O(h^2), one order higher than its interpolation error when the exact solution belongs to H^3(Ω). However, the interpolation error and consistency error of Carey element are of order O(h). It seems that the above special property has never been seen for other triangular elements for the second order problems. 相似文献
10.
CHENWei 《系统科学与复杂性》2003,16(1):101-103
The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density.The electric potential equation is discretized by the finite element method.The electron and hole density equations are treated by implicit-explicit multistep finite element methods.The optimal L^2-norm error estimates are derived. 相似文献
11.
<正> In this paper,a two-scale finite element approach is proposed and analyzed for approximationsof Green's function in three-dimensions.This approach is based on a two-scale finite elementspace defined,respectively,on the whole domain with size H and on some subdomain containing singularpoints with size h (h H).It is shown that this two-scale discretization approach is very efficient.In particular,the two-scale discretization approach is applied to solve Poisson-Boltzmann equationssuccessfully. 相似文献
12.
Elliptic PDE-constrained optimal control problems with L1-control cost (L1-EOCP) are considered. To solve L1-EOCP, the primal-dual active set (PDAS) method, which is a special semismooth Newton (SSN) method, used to be a priority. However, in general solving Newton equations is expensive. Motivated by the success of alternating direction method of multipliers (ADMM), we consider extending the ADMM to L1-EOCP. To discretize L1-EOCP, the piecewise linear finite element (FE) is considered. However, different from the finite dimensional l1-norm, the discretized L1-norm does not have a decoupled form. To overcome this difficulty, an effective approach is utilizing nodal quadrature formulas to approximately discretize the L1-norm and L2-norm. It is proved that these approximation steps will not change the order of error estimates. To solve the discretized problem, an inexact heterogeneous ADMM (ihADMM) is proposed. Different from the classical ADMM, the ihADMM adopts two different weighted inner products to define the augmented Lagrangian function in two subproblems, respectively. Benefiting from such different weighted techniques, two subproblems of ihADMM can be efficiently implemented. Furthermore, theoretical results on the global convergence as well as the iteration complexity results o(1/k) for ihADMM are given. In order to obtain more accurate solution, a two-phase strategy is also presented, in which the primal-dual active set (PDAS) method is used as a postprocessor of the ihADMM. Numerical results not only confirm error estimates, but also show that the ihADMM and the two-phase strategy are highly efficient. 相似文献
13.
在基于漂移扩散模型的半导体器件仿真模拟中,采用Zlamal有限元方法进行数值离散,结合提出的电离损伤耦合模型,对横向PNP(LPNP)双极晶体管(BJT,bipolarjunction transistors)的电离损伤效应进行模拟。基于三维并行自适应有限元软件平台PHG(Parallel Hierarchical Grid)实现了模型和算法,并通过数值计算的方式成功模拟出了LPNP受电离辐射影响后出现的基极电流增大及电流增益退化的现象。进行了网格规模达1亿单元、并行规模达1024进程的大规模数值实验,展示了算法良好的并行可扩展性。 相似文献
14.
YUANYirang 《系统科学与复杂性》2004,17(4):538-554
For the transient behavior of a semiconductor device, the modified method of characteristics with alternating-direction finite element procedures for nonrectangular region is put forward. Some techniques, such as calculus of variations, isoparametric transformation, patch approximation, operator-splitting, characteristic method, symmetrical reflection, energy method, negative norm estimate and a prior estimates and techniques, are employed. In the nonrectangular region case, optimal order estimates in L2 norm are derived for the error in the approximation solution. Thus the well-known theoretical problem has been thoroughly and completely solved. 相似文献
15.
<正> This work is concerned with rates of convergence of numerical methods using Markov chainapproximation for controlled diffusions with stopping (the first exit time from a bounded region).In lieuof considering the associated finite difference schemes for Hamilton-Jacobi-Bellman (HJB) equations,a purely probabilistic approach is used.There is an added difficulty due to the boundary condition,which requires the continuity of the first exit time with respect to the discrete parameter.To prove theconvergence of the algorithm by Markov chain approximation method,a tangency problem might arise.A common approach uses certain conditions to avoid the tangency problem.Here,by modifying thevalue function,it is demonstrated that the tangency problem will not arise in the sense of convergencein probability and in L~1.In addition,controlled diffusions with a discount factor is also treated. 相似文献
16.
<正> This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vriesequation posed on a finite interval with general nonhomogeneous boundary conditions.Using thestrong Kato smoothing property of the associated linear problem,the IBVP is shown to be locallywell-posed in the space H~s(0,1) for any s≥0 via the contraction mapping principle. 相似文献
17.
This paper considers the mixed covolume method for the second-order elliptic equations over quadrilaterals.Superconvergence results are established in this paper on quadrilateral grids satisfying the h~2-parallelogram condition when the lowest-order Raviart-Thomas space is employed in the mixed covolume method.The authors prove O(h~2) accuracy between the approximate velocity or pressure and a suitable projection of the real velocity or pressure in the L~2 norm.Numerical experiments illustrating the theoretical results are provided. 相似文献
18.
Yuhong Li 《系统科学与复杂性》2008,21(3):416-426
Given a real-valued separable M-type 2 Banach space X with the p-th power of the norm of C2-class, the almost sure asymptotic upper bounds of the solutions of the Ornstein-Uhlenbeck Processes described by the following equations {dz(t)=A(t,z(t))dt+σ(t,z(t))dW(t),z(0)=z0∈X,are investigated. This study generalizes the corresponding well-known finite dimensional results of Lapeyre (1989) and Mao (1992). 相似文献
19.
This paper proposes to use the blockwise empirical likelihood(EL) method to construct the confidence regions for the regression vector β in a partially linear model under negatively associated errors. It is shown that the blockwise EL ratio statistic for β is asymptotically χ~2 distributed. The result is used to obtain an EL-based confidence region for β. Results of a simulation study on the finite sample performance of the proposed confidence regions are reported. 相似文献