共查询到20条相似文献,搜索用时 15 毫秒
1.
Yirang Yuan 《Numerical Methods for Partial Differential Equations》2008,24(2):400-417
The mathematical model of the three‐dimensional semiconductor devices of heat conduction is described by a system of four quasi‐linear partial differential equations for initial boundary value problem. One equation of elliptic form is for the electric potential; two equations of convection‐dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Upwind finite difference fractional step methods are put forward. Some techniques, such as calculus of variations, energy method multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates and techniques are adopted. Optimal order estimates in L2 norm are derived to determine the error in the approximate solution.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 相似文献
2.
Yirang Yuan 《Numerical Methods for Partial Differential Equations》2007,23(5):1037-1058
For nonlinear coupled system of multilayer dynamics of fluids in porous media, a second‐order upwind finite‐difference fractional‐steps scheme applicable to parallel arithmetic are put forward, and two‐ and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high‐order difference operators, and prior estimates are adopted. Optimal order estimates in l2 norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of migration‐accumulation of oil resources. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
3.
Yirang Yuan 《Numerical Methods for Partial Differential Equations》2003,19(5):665-681
For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L2 norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003. 相似文献
4.
N. I. Mahmudov 《Mathematical Methods in the Applied Sciences》2011,34(13):1618-1626
In this paper we give the estimates of the central moments for the limit q‐Bernstein operators. We introduce the higher order generalization of the limit q‐Bernstein operators and using the moment estimations study the approximation properties of these newly defined operators. It is shown that the higher order limit q‐Bernstein operators faster than the q‐Bernstein operators for the smooth functions defined on [0, 1]. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
5.
In this paper, commutativity of kth‐order slant Toeplitz operators are discussed. We show that commutativity and essential commutativity of two slant Toeplitz operators are the same. Also, we study kth‐order slant Toeplitz operators on the Bergman space L2a(D) and give some commuting properties, algebraic and spectral properties of kth‐order slant Toeplitz operators on the Bergman space (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
Hui Guo Hongfei Fu Jiansong Zhang 《Numerical Methods for Partial Differential Equations》2014,30(1):222-238
This article studies superconvergence phenomena of the split least‐squares mixed finite element method for second‐order hyperbolic equations. By selecting the least‐squares functional properly, the procedure can be split into two independent symmetric positive definite subprocedures, one of which is for the primitive unknown and the other is for the flux. Based on interpolation operators and an auxiliary projection, superconvergent H1 error estimates for the primary variable u and L2 error estimates for the introduced flux variable σ are obtained under the standard quasiuniform assumptions on finite element partition. A numerical example is given to show the performance of the introduced scheme. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 222‐238, 2014 相似文献
7.
《Mathematische Nachrichten》2017,290(16):2459-2511
In this paper we establish square‐function estimates on the double and single layer potentials for divergence form elliptic operators, of arbitrary even order 2m , with variable t‐independent coefficients in the upper half‐space. This generalizes known results for variable‐coefficient second‐order operators, and also for constant‐coefficient higher‐order operators. 相似文献
8.
The upwind finite difference fractional steps method for combinatorial system of dynamics of fluids in porous media and its application 总被引:4,自引:0,他引:4
袁益让 《中国科学A辑(英文版)》2002,45(5):578-593
For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite
difference fractional steps schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional
schemes are used to form a complete set. Some techniques, such as implicit-explicit difference scheme, calculus of variations,
multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates,
are adopted. Optimal order estimates in L
2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to
the numerical simulation of migration-accumulation of oil resources. Keywords: combinatorial system, multilayer dynamics of
fluids in porous media, two-class upwind finite difference fractional steps method, convergence, numerical simulation of energy
sources. 相似文献
9.
The characteristic finite difference fractional steps methods for compressible two-phase displacement problem 总被引:3,自引:0,他引:3
Yirang Yuan 《中国科学A辑(英文版)》1999,42(1):48-57
For compressible two-phase displacement problem, a kind of characteristic finite difference fractional steps schemes is put
forward and thick and thin grids are used to form a complete set. Some techniques, such as piecewise biquadratic interpolation,
of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference
operators and prior estimates are adopted. Optimal order estimates inL
2 norm are derived to determine the error in the approximate solution.
Project supported by the National Scaling Program, the National Tackling Key Problems Program and the Doctorate Foundation
of the State Education Commission of China. 相似文献
10.
Yasuo Komori 《Mathematische Nachrichten》2003,259(1):42-50
We define weak Herz spaces (?n) which are the weak version of the ordinary Herz spaces (?n). We consider the boundedness of Calderón‐Zygmund operators from to at critical indexes α = ?n/q, n(1? 1/q) and q = 1. We also consider weighted estimates. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
We prove the existence of solutions for some semilinear elliptic equations in the appropriate H4 spaces using the fixed‐point technique where the elliptic equation contains fourth‐order differential operators with and without Fredholm property, generalizing the previous results. 相似文献
12.
Zhangxin Chen 《Numerical Methods for Partial Differential Equations》2002,18(2):203-217
In this article we prove uniform convergence estimates for the recently developed Galerkin‐multigrid methods for nonconforming finite elements for second‐order problems with less than full elliptic regularity. These multigrid methods are defined in terms of the “Galerkin approach,” where quadratic forms over coarse grids are constructed using the quadratic form on the finest grid and iterated coarse‐to‐fine intergrid transfer operators. Previously, uniform estimates were obtained for problems with full elliptic regularity, whereas these estimates are derived with less than full elliptic regularity here. Applications to the nonconforming P1, rotated Q1, and Wilson finite elements are analyzed. The result applies to the mixed method based on finite elements that are equivalent to these nonconforming elements. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 203–217, 2002; DOI 10.1002/num.10004 相似文献
13.
In this paper, weak (1,1) and Lp estimates for the parabolic Littlewood–Paley operators on some homogeneous spaces are established, which are extensions of known results. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
We apply the Bennett–Carbery–Tao multilinear restriction estimate in order to bound restriction operators and more general
oscillatory integral operators. We get improved L
p
estimates in the Stein restriction problem for dimension at least 5 and a small improvement in dimension 3. We prove similar
estimates for H?rmander-type oscillatory integral operators when the quadratic term in the phase function is positive definite,
getting improvements in dimension at least 5. We also prove estimates for H?rmander-type oscillatory integral operators in
even dimensions. These last oscillatory estimates are related to improved bounds on the dimensions of curved Kakeya sets in
even dimensions. 相似文献
15.
Zhiyue Zhang Dingwen Deng 《Numerical Methods for Partial Differential Equations》2007,23(6):1530-1559
A modified backward difference time discretization is presented for Galerkin approximations for nonlinear hyperbolic equation in two space variables. This procedure uses a local approximation of the coefficients based on patches of finite elements with these procedures, a multidimensional problem can be solved as a series of one‐dimensional problems. Optimal order H01 and L2 error estimates are derived. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
16.
Liming Guo Ziping Huang Cheng Wang 《Numerical Methods for Partial Differential Equations》2014,30(3):813-837
In this article, we study the edge residual‐based a posteriori error estimates of conforming linear finite element method for nonmonotone quasi‐linear elliptic problems. It is proven that edge residuals dominate a posteriori error estimates. Up to higher order perturbations, edge residuals can act as a posteriori error estimators. The global reliability and local efficiency bounds are established both in H 1‐norm and L 2‐norm. Numerical experiments are provided to illustrate the performance of the proposed error estimators. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 813–837, 2014 相似文献
17.
Shagufta Rahman Mohammad Mursaleen Ana Maria Acu 《Mathematical Methods in the Applied Sciences》2019,42(11):4042-4053
In the present article, Kantorovich variant of λ‐Bernstein operators with shifted knots are introduced. The advantage of using shifted knot is that one can do approximation on [0,1] as well as on its subinterval. In addition, it adds flexibility to operators for approximation. Some basic results for approximation as well as rate of convergence of the introduced operators are established. The rth order generalization of the operator is also discussed. Further for comparisons, some graphics and error estimation tables are presented using MATLAB. 相似文献
18.
Mingxia Li Shipeng Mao Shangyou Zhang 《Mathematical Methods in the Applied Sciences》2014,37(7):937-951
In this paper, we revisit the classical error estimates of nonconforming Crouzeix–Raviart type finite elements for the Stokes equations. By introducing some quasi‐interpolation operators and using the special properties of these nonconforming elements, it is proved that their consistency errors can be bounded by their approximation errors together with a high‐order term, especially which can be of arbitrary order provided that f in the right‐hand side is piecewise smooth enough. Furthermore, we show an interesting result that both in the energy norm and L2 norm the consistency errors are dominated by the approximation errors of their finite element spaces. As byproducts, we derive the error estimates in both energy and L2 norms under the regularity assumption ( u ,p) ∈ H 1 + s(Ω) × Hs(Ω) with any s ∈ (0,1], which fills the gap in the a priori error estimate of these nonconforming elements with low regularity . Furthermore, a robust convergence is proved with minimal regularity assumption s = 0. These results seem to be missing in the literature. Numerical tests are provided, confirming the analysis, especially the new results on the L2 convergence. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
19.
M. W. Wong 《Mathematische Nachrichten》2006,279(3):319-326
We construct the minimal and maximal extensions in L p (?n ), 1 < p < ∞, for M ‐elliptic pseudo‐differential operators initiated by Garello and Morando. We prove that they are equal and determine the domains of the minimal, and hence maximal, extensions of M ‐elliptic pseudo‐differential operators. For M ‐elliptic pseudodifferential operators with constant coefficients, the spectra and essential spectra are computed. An application to quantization is given. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
《Mathematical Methods in the Applied Sciences》2018,41(10):3588-3604
We consider the periodic problem for 2‐fluid nonisentropic Euler‐Poisson equations in semiconductor. By choosing a suitable symmetrizers and using an induction argument on the order of the time‐space derivatives of solutions in energy estimates, we obtain the global stability of solutions with exponential decay in time near the nonconstant steady‐states for 2‐fluid nonisentropic Euler‐Poisson equations. This improves the results obtained for models with temperature diffusion terms by using the pressure functions pν in place of the unknown variables densities nν. 相似文献