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1.
Cell Conservative Flux Recovery and a Posteriori Error Estimate of Vertex-Centered Finite Volume Methods
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Long Chen & Ming Wang 《advances in applied mathematics and mechanics.》2013,5(5):705-727
A cell conservative flux recovery technique is developed here for vertex-centered
finite volume methods of second order elliptic equations.
It is based on solving a local Neumann problem on each control volume using mixed
finite element methods. The recovered flux is used to
construct a constant free a posteriori error estimator which is proven to be
reliable and efficient. Some numerical tests are presented
to confirm the theoretical results. Our method works for general order finite volume
methods and the recovery-based and residual-based
a posteriori error estimators are the first result on
a posteriori error estimators for high
order finite volume methods. 相似文献
2.
A Posteriori Error Estimates of Triangular Mixed Finite Element Methods for Semilinear Optimal Control Problems
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In this paper, we present an a posteriori error estimates of semilinear
quadratic constrained optimal control problems using triangular mixed finite element
methods. The state and co-state are approximated by the order $k\leq 1$ Raviart-
Thomas mixed finite element spaces and the control is approximated by piecewise
constant element. We derive a posteriori error estimates for the coupled state and
control approximations. A numerical example is presented in confirmation of the
theory. 相似文献
3.
Jianwei Zhou 《advances in applied mathematics and mechanics.》2015,7(2):145-157
In this paper, the Chebyshev-Galerkin spectral approximations are employed to investigate Poisson equations and the fourth order equations in one dimension. Meanwhile, $p$-version finite element methods with Chebyshev polynomials are utilized to solve Poisson equations. The efficient and reliable a posteriori error estimators are given for different models. Furthermore, the a priori error estimators are derived independently. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error indicators and a priori error estimations. 相似文献
4.
A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems
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Wanfang Shen Liang Ge Danping Yang & Wenbin Liu 《advances in applied mathematics and mechanics.》2014,6(5):552-569
In this paper, we study the mathematical formulation for an optimal
control problem governed by a linear parabolic integro-differential
equation and present the optimality conditions. We then set up its
weak formulation and the finite element approximation scheme. Based
on these we derive the a priori error estimates for its finite
element approximation both in $H^1$ and $L^2$ norms. Furthermore, some numerical tests are presented to
verify the theoretical results. 相似文献
5.
A Posteriori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for a Kind of Compressible Miscible Displacement Problems
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A kind of compressible miscible displacement problems which include
molecular diffusion and dispersion in porous media are investigated.
The mixed finite element method is applied to the flow equation, and the
transport one is solved by the symmetric interior penalty
discontinuous Galerkin method. Based on a duality argument,
employing projection estimates and approximation properties, a
posteriori residual-type $hp$ error estimates for the coupled system
are presented, which is often used for guiding adaptivity. Comparing
with the error analysis carried out by Yang (Int. J. Numer. Meth.
Fluids, 65(7) (2011), pp. 781-797), the current work is more
complicated and challenging. 相似文献
6.
Samir Karaa 《advances in applied mathematics and mechanics.》2011,3(2):181-203
In this paper, we investigate the stability and convergence of a family of
implicit finite difference schemes in time and Galerkin finite element methods in
space for the numerical solution of the acoustic wave equation. The schemes cover
the classical explicit second-order leapfrog scheme and the fourth-order accurate
scheme in time obtained by the modified equation method. We derive general stability
conditions for the family of implicit schemes covering some well-known CFL
conditions. Optimal error estimates are obtained. For sufficiently smooth solutions,
we demonstrate that the maximal error in the $L^2$-norm error over a finite time interval
converges optimally as $\mathcal{O}(h^{p+1}+∆t^s)$, where $p$ denotes the polynomial degree, $s$=2 or 4, $h$ the mesh size, and $∆t$ the time step. 相似文献
7.
Posteriori Error Estimation for an Interior Penalty Discontinuous Galerkin Method for Maxwell's Equations in Cold Plasma
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Jichun Li 《advances in applied mathematics and mechanics.》2009,1(1):107-124
In this paper, we develop a residual-based a posteriori error
estimator for the time-dependent Maxwell's equations in the cold
plasma. Here we consider a semi-discrete interior penalty
discontinuous Galerkin (DG) method for solving the governing
equations. We provide both the upper bound and lower bound analysis
for the error estimator. This is the first posteriori error analysis
carried out for the Maxwell's equations in dispersive media. 相似文献
8.
Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations
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Huipo Liu Shuanghu Wang & Hongbin Han 《advances in applied mathematics and mechanics.》2016,8(5):871-886
In this paper, we consider a least squares nonconforming finite element of
low order for solving the transport equations. We give a detailed overview on the stability
and the convergence properties of our considered methods in the stability norm.
Moreover, we derive residual type a posteriori error estimates for the least squares
nonconforming finite element methods under $H^{−1}$-norm, which can be used as the error
indicators to guide the mesh refinement procedure in the adaptive finite element
method. The theoretical results are supported by a series of numerical experiments. 相似文献
9.
Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters
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Yanping Chen Haitao Leng & Li-Bin Liu 《advances in applied mathematics and mechanics.》2015,7(2):196-206
In this paper, we consider a singularly perturbed convection-diffusion problem.
The problem involves two small parameters that gives rise to two boundary layers
at two endpoints of the domain. For this problem, a non-monotone finite element
methods is used. A priori error bound in the maximum norm is obtained. Based on
the a priori error bound, we show that there exists Bakhvalov-type mesh that gives
optimal error bound of$\mathcal{O}(N^{−2})$ which is robust with respect to the two perturbation
parameters. Numerical results are given that confirm the theoretical result. 相似文献
10.
11.
痕量元素分析中的随机误差的估计 总被引:3,自引:0,他引:3
本文讨论了痕量元素分析中的随机误差的规律性。文中对专家们提出的各种误差分布模型进行了比较和分析。采用12个标准物质样品的23种痕量元素的大量分析数据,对痕量分析的相对标准偏差和含量的关系进行了不同模型的研究,并由此得到相应的数学表达式,用于控制痕量分析中的随机误差,数学表达式表明了检出限,含量和随机误差的关系,采用此数学表达式对23种痕量元素的4万余个分析数据进行了检验,结果和我们预期的结论相当吻合。 相似文献
12.
Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations
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Tianliang Hou & Li Li 《advances in applied mathematics and mechanics.》2016,8(6):1050-1071
In this paper, we investigate the error estimates of mixed finite element
methods for optimal control problems governed by general elliptic equations. The
state and co-state are approximated by the lowest order Raviart-Thomas mixed finite
element spaces and the control variable is approximated by piecewise constant functions.
We derive $L^2$ and $H^{-1}$-error estimates both for the control variable and the state
variables. Finally, a numerical example is given to demonstrate the theoretical results. 相似文献
13.
Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity
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Yanping Chen Tianliang Hou & Weishan Zheng 《advances in applied mathematics and mechanics.》2012,4(6):751-768
In this paper, we investigate the error estimates and
superconvergence property of mixed finite element methods for
elliptic optimal control problems. The state and co-state are
approximated by the lowest order Raviart-Thomas mixed finite element
spaces and the control variable is approximated by piecewise
constant functions. We derive $L^2$ and $L^\infty$-error
estimates for the control variable. Moreover, using a recovery
operator, we also derive some superconvergence results for the
control variable. Finally, a numerical example is given to
demonstrate the theoretical results. 相似文献
14.
This paper is concerned with a stabilized finite element method
based on two local Gauss integrations for the two-dimensional
non-stationary conduction-convection 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. 相似文献
15.
流动数值模拟中一种并行自适应有限元算法 总被引:1,自引:0,他引:1
给出了一种流动数值模拟中的基于误差估算的并行网格自适应有限元算法.首先,以初网格上获得的当地事后误差估算值为权,应用递归谱对剖分方法划分初网格,使各子域上总体误差近似相等,以解决负载平衡问题.然后以误差值为判据对各子域内网格进行独立的自适应处理.最后应用基于粘接元的区域分裂法在非匹配的网格上求解N-S方程.区域分裂情形下N-S方程有限元解的误差估算则是广义Stokes问题误差估算方法的推广.为验证方法的可靠性,给出了不可压流经典算例的数值结果. 相似文献
16.
An Inf-Sup Stabilized Finite Element Method by Multiscale Functions for the Stokes Equations
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Zhihao Ge Yinnian He & Lingyu Song 《advances in applied mathematics and mechanics.》2009,1(2):273-287
In the paper, an inf-sup stabilized finite element method by multiscale
functions for the Stokes equations is discussed. The key idea is to use a Petrov-Galerkin approach based on the enrichment of the standard polynomial space for
the velocity component with multiscale functions. The inf-sup condition for $P_1$-$P_0$ triangular element (or $Q_1$-$P_0$ quadrilateral element) is established. And the optimal
error estimates of the stabilized finite element method for the Stokes equations
are obtained. 相似文献
17.
发展了一种广义Stokes问题的无覆盖区域分裂解法。子域交界面上的约束条件是通过引入一Lagrange乘子而得到弱满足的,在有限元离散子域的交界处网格可以是非匹配的。应用Petrov Galerkin方法解每个子域上的广义Stokes问题,而交界面上的Lagrange乘子则通过共轭梯度法迭代求解,各变量均由线性函数离散。对上述区域分裂解法,还构造了基于求解当地问题的误差事后估算方法。各变量的当地误差估算器定义在二阶非连续鼓包(bump)函数的空间中。最后给出了基于事后误差估算值的自适应网格上的数值结果。 相似文献
18.
An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations
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Ying Yang & Benzhuo Lu 《advances in applied mathematics and mechanics.》2013,5(1):113-130
Poisson-Nernst-Planck
equations are a coupled system of nonlinear partial differential
equations consisting of the Nernst-Planck equation and
the electrostatic Poisson equation with delta distribution sources,
which describe the electrodiffusion of ions in a solvated
biomolecular system. In this paper, some error bounds for a piecewise
finite element approximation to this problem are derived. Several numerical
examples including biomolecular problems are shown to support our analysis. 相似文献
19.
A Priori and a Posteriori Error Analysis of the Discontinuous Galerkin Methods for Reissner-Mindlin Plates
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Jun Hu & Yunqing Huang 《advances in applied mathematics and mechanics.》2011,3(6):649-662
In this paper, we apply an a posteriori error control theory that
we develop in a very recent paper to three families of the discontinuous Galerkin methods for the
Reissner-Mindlin plate problem. We derive robust a posteriori error
estimators for them and prove their reliability and efficiency. 相似文献
20.
Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions
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In this paper, we present two-level defect-correction finite element method
for steady Navier-Stokes equations at high Reynolds number with the friction boundary
conditions, which results in a variational inequality problem of the second kind.
Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes
type on the coarse mesh and solve a variational inequality problem of Navier-Stokes
type corresponding to Newton linearization on the fine mesh. The error estimates
for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm are derived.
Finally, the numerical results are provided to confirm our theoretical analysis. 相似文献