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A UNIFIED A POSTERIORI ERROR ANALYSIS FOR DISCONTINUOUS GALERKIN APPROXIMATIONS OF REACTIVE TRANSPORT EQUATIONS

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Journal of Computational Mathematics 2006年第3期24卷 425-434页

作者： Ji-ming yang yan-ping chen Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied Mathematics and School of Mathematics and Computing Science Xiangtan University Xiangtan 4 11105 China

Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Galerkin （SIPG）, and incomplete interior penalty Galerkin （IIPG）. A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution and given data, explicit estimators can be computed efficiently and directly, which can be used as error indicators for adaptation. Unlike in the reference [10], we obtain the error estimators in L^2 （L^2） norm by using duality techniques instead of in L^2（H^1） norm.

关键词： A posteriori error estimates Duality techniques Discontinuous Galerkin methods

IMPROVED ERROR ESTIMATES FOR MIXED FINITE ELEMENT FOR NONLINEAR HYPERBOLIC EQUATIONS: THE CONTINUOUS-TIME CASE

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Journal of Computational Mathematics 2001年第4期19卷 385-392页

作者： yan-ping chen Yun-qing Huang Xiangtan Univ Dept Math Xiangtan 411105 Peoples R China

Presents a study which computed the L sup2-error estimates for mixed finite element methods for second order nonlinear hyperbolic equations. Application of computed results to a continuous-time case; Demonstration of ... 详细信息

关键词： nonlinear hyperbolic equations mixed finite element methods error estimates superconvergence

Complete Convergence for Randomly Weighted Sums of Random Variables Satisfying Some Moment Inequalities

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Acta Mathematica Sinica,English Series 2021年第2期37卷 279-288页

作者： ping yan chen Soo Hak SUNG Department of Mathematics Ji'nan UniversityGuangzhou 510630P.R.China Department of Applied Mathematics Pai Chai UniversityDaejeon 35345South Korea

For random variables and random weights satisfying Marcinkiewicz-Zygmund and Rosenthal type moment inequalities, we establish complete convergence results for randomly weighted sums of the random variables. Our results generalize those of(Thanh et al. SIAM J. Control Optim., 49,106–124(2011), Han and Xiang J. Ineq. Appl., 2016, 313(2016), Li et al. J. Ineq. Appl., 2017, 182(2017), and Wang et al. Statistics, 52, 503–518(2018).)

关键词： Randomly weighted sum complete convergence moment inequality

Convergence Rates for Probabilities of Moderate Deviations for Moving Average Processes

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Acta Mathematica Sinica,English Series 2008年第4期24卷 611-622页

作者： ping yan chen Ding cheng WANG Department of Mathematics Jinan University Guangzhou 510630 P. R. China Center of Financial Mathematics MSI Australian National University Canberra Act 0200 Australia School of Applied Mathematics University of Electronic Science and Technology of ChinaChengdu 610054 P. R. China

The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates （or complete moment convergence） for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.

关键词： complete convergence complete moment convergence moderate deviation law of the iterated logarithm invariance principle moving average process

Complete Moment Convergence for Sequence of Identically Distributed φ-mixing Random Variables

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Acta Mathematica Sinica,English Series 2010年第4期26卷 679-690页

作者： ping yan chen Ding cheng WANG Department of Mathematics Ji'nan University Guangzhou 510630 P. R. China Center of Financial Mathematics MSI Australian National UniversityCanberra Act 0200 Australia School of Applied Mathematics University of Electronic Science and Technology of China Chengdu 610054 P. R. China

In the paper we extend and generalize some results of complete moment convergence results （or the refinement of complete convergence） obtained by Chow [On the rate of moment complete convergence of sample sums and extremes. Bull. Inst. Math. Academia Sinica, 16, 177-201 （1988）] and Li ＆ Spataru [Refinement of convergence rates for tail probabilities. J. Theor. Probab., 18, 933-947 （2005）] to sequences of identically distributed φ-mixing random variables.

关键词： complete convergence complete moment convergence φ-mixing

L^r Convergence for B-valued Random Elements

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Acta Mathematica Sinica,English Series 2012年第4期28卷 857-868页

作者： ping yan chen Ding cheng WANG Department of Mathematics Ji'nan University School of Applied Mathematics University of Electronic Science and Technology of China

The paper investigates Lp convergence and Marcinkiewicz-Zygmund strong laws of large numbers for random elements in a Banach space under the condition that the Banach space is of Rademacher type p, 1 〈 p 〈 2. The paper also discusses Lτ convergence and Lτ bound for random elements without any geometric restriction condition on the Banach space.

关键词： Lτ convergence random element Rademacher type p Marcinkiewicz Zygmund stronglaw of large number

Complete and Complete Moment Convergence for Weighted Sums of Widely Orthant Dependent Random Variables

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Acta Mathematica Sinica,English Series 2014年第9期30卷 1539-1548页

作者： De Hua QIU ping yan chen School of Mathematics and Statistics Guangdong University of Finance & Economics Department of Mathematics Jinan University

In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the corresponding results for weighted sums of extended negatively orthant dependent random variables are also obtained, which generalize and improve the related known works in the literature.

关键词： Widely orthant dependent random variables extended negatively orthant dependent random variables complete convergence complete moment convergence

The Commutator of the Kato Square Root for Second Order Elliptic Operators on R^n

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Acta Mathematica Sinica,English Series 2016年第10期32卷 1121-1144页

作者： yan ping chen Yong DING Steve HOFMANN Department of Applied Mathematics School of Mathematics and PhysicsUniversity of Science and Technology Beijing School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex Systems(BNU)Ministry of Education Department of Mathematics University of Missouri

Let L = -div（AV） be a second order divergence form elliptic operator, and A be an accretive, n × n matrix with bounded measurable complex coefficients in R^n. We obtain the Lp bounds for the commutator generated by the Kato square root v/L and a Lipschitz function, which recovers a previous result of Calderon, by a different method. In this work, we develop a new theory for the commutators associated to elliptic operators with Lipschitz function. The theory of the commutator with Lipschitz function is distinguished from the analogous elliptic operator theory.

关键词： Commutator Kato square root Lipschitz function elliptic operators

Commutators of Marcinkiewicz Integral with Rough Kernels on Sobolev Spaces

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Acta Mathematica Sinica,English Series 2011年第7期27卷 1345-1366页

作者： yan ping chen Yong DING Xin Xia WANG Department of Mathematics and Mechanics School of Applied ScienceUniversity of Science and Technology of Beijing Beijing 100083 P. R. China School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex Systems (BNU) Ministry of Education Beijing 100875 P. R. China The College of Mathematics and Systems Science Xinjiang University U~'umqi 830046 P. R. China

In this paper, the authors give the boundedness of the commutator [b,μΩ,γ] from the homogeneous Sobolev space LP（R^n） to the Lebesgue space L^p（R^n） for 1 〈 p 〈 ∞, where μΩ,γ denotes the Marcinkiewicz integral with rough hypersingular kernel defined by μΩ,γf（x）=（∫0^∞｜∫｜x-y｜≤tΩ（x-y）/｜x-y｜^n-1f（y）dy｜^2dt/t^3＋2γ）^1/2,with Ω∈L^1（S^n-1）for 0〈γ〈min（n/2,n/p）or Ω∈L（log＋L）^β（S^n-1）for｜1-2/p｜〈β〈1（0〈γ〈n/2）,respectively.

关键词： Marcinkiewicz integral commutator rough kernel Sobolev space Bony paraproduct