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P_1-nonconforming triangular finite element method for elliptic and parabolic interface problems

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Applied Mathematics and Mechanics(English Edition) 2015年第9期36卷 1197-1212页

作者： Hongbo GUAN dongyang shi College of Mathematics and Information Sciences Zhengzhou University of Light Industry School of Mathematics and Statistics Zhengzhou University

The lowest order Pl-nonconforming triangular finite element method （FEM） for elliptic and parabolic interface problems is investigated. Under some reasonable regularity assumptions on the exact solutions, the optimal order error estimates are obtained in the broken energy norm. Finally, some numerical results are provided to verify the theoretical analysis.

关键词： P1-nonconforming finite element method (FEM) interface problem opti-mal order error estimate

A LOW ORDER NONCONFORMING ANISOTROPIC FINITE ELEMENT APPROXIMATION TO PARABOLIC PROBLEM

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Journal of Systems Science & Complexity 2009年第3期22卷 518-532页

作者： dongyang shi Wei GONG Department of Mathematics Zhengzhou University Zhengzhou 450052 China. Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190 China.

A low order nonconforming finite element is applied to the parabolic problem with *** the semidiscrete and fully discrete forms are *** superclose properties andsuperconvergence are obtained through some novel approac... 详细信息

关键词： Anisotropic meshes nonconforming element parabolic problem superclose superconveygence.

AN ANISOTROPIC NONCONFORMING FINITE ELEMENT SCHEME WITH MOVING GRIDS FOR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

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Journal of Systems Science & Complexity 2011年第5期24卷 1020-1032页

作者： dongyang shi Lin WANG Department of Mathematics Zhengzhou University Zhengzhou 450052 China Department of Basic Henan Mechanical and Electrical Engineering College Xinxiang 453002 China

A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis is presented and the error estimates are obtained by using the interpolation operator instead of the conventional elliptic projection which is an indispensable tool in the convergence analysis of traditional finite element methods in previous literature.

关键词： Anisotropic meshes error estimates moving grids nonconforming finite element parabolicintegro-differential equations

CONVERGENCE ANALYSIS OF NONCONFORMING QUADRILATERAL FINITE ELEMENT METHODS FOR NONLINEAR COUPLED SCHRODINGER-HELMHOLTZ EQUATIONS

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Journal of Computational Mathematics 2024年第4期42卷 979-998页

作者： dongyang shi Houchao Zhang School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China

The focus of this paper is on two novel linearized Crank-Nicolson schemes with nonconforming quadrilateral finite element methods(FEMs)for the nonlinear coupled Schrodinger-Helmholtz *** L^(2) and H^(1) estimates of orders O(h^(2)+τ^(2))and O(h^(2)+τ^(2))are derived respectively without any grid-ratio condition through the following two *** is that a time-discrete system is introduced to split the error into the temporal error and the spatial error,which leads to optimal temporal error estimates of order O(τ^(2))in L^(2) and the broken H^(1)-norms,as well as the uniform boundness of numerical solutions in L^(∞) *** other is that a novel projection is utilized,which can iron out the difficulty of the existence of the consistency *** leads to derive optimal spatial error estimates of orders O(h^(2))in L^(2)-norm and O(h)in the broken H^(1)-norm under the H^(2) regularity of the solutions for the time-discrete *** last,two numerical examples are provided to confirm the theoretical ***,h is the subdivision parameter,and τ is the time step.

关键词： Schrodinger-Helmholtz equations Nonconforming FEMs Linearized Crank-Nicolson scheme Optimal error estimates

UNCONDITIONALLY OPTIMAL ERROR ESTIMATES OF THE BILINEAR-CONSTANT SCHEME FOR TIME-DEPENDENT NAVIER-STOKES EQUATIONS

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Journal of Computational Mathematics 2022年第1期40卷 127-146页

作者： Huaijun Yang dongyang shi School of Mathematics Zhengzhou University of AeronauticsZhengzhou 450046China School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China

In this paper,the unconditional error estimates are presented for the time-dependent Navier-Stokes equations by the bilinear-constant *** corresponding optimal error estimates for the velocity and the pressure are derived unconditionally,while the previous works require certain time-step *** analysis is based on an iterated time-discrete system,with which the error function is split into a temporal error and a spatial *** τ-independent(τ is the time stepsize)error estimate between the numerical solution and the solution of the time-discrete system is proven by a rigorous analysis,which implies that the numerical solution in L^(∞)-norm is *** optimal error estimates can be obtained in a traditional *** results are provided to confirm the theoretical analysis.

关键词： Navier-Stokes equations Unconditionally optimal error estimates Bilinear-constant scheme Time-discrete system.

UNIFORM SUPERCONVERGENCE ANALYSIS OF A TWO-GRID MIXED FINITE ELEMENT METHOD FOR THE TIME-DEPENDENT BI-WAVE PROBLEM MODELING D-WAVE SUPERCONDUCTORS

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Journal of Computational Mathematics 2024年第2期42卷 415-431页

作者： Yanmi Wu dongyang shi PLA Information Engineering University Zhengzhou 450001China School of Mathematics and Information Sciences Yantai UniversityYantai 264005China

In this paper,a two-grid mixed finite element method(MFEM)of implicit Backward Euler(BE)formula is presented for the fourth order time-dependent singularly perturbed Bi-wave problem for d-wave superconductors by the nonconforming EQ_(1)^(rot) *** this approach,the original nonlinear system is solved on the coarse mesh through the Newton iteration method,and then the linear system is computed on the fine mesh with Taylor’s *** on the high accuracy results of the chosen element,the uniform superclose and superconvergent estimates in the broken H^(1)-norm are derived,which are independent of the negative powers of the perturbation parameter appeared in the considered *** results illustrate that the computing cost of the proposed two-grid method is much less than that of the conventional Galerkin MFEM without loss of accuracy.

关键词： Time-dependent Bi-wave problem Two-grid mixed finite element method Uniform superclose and superconvergent estimates

SUPERCONVERGENCE ANALYSIS OF A BDF-GALERKIN FEM FOR THE NONLINEAR KLEIN-GORDON-SCHRODINGER EQUATIONS WITH DAMPING MECHANISM

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Journal of Computational Mathematics 2023年第2期41卷 224-245页

作者： dongyang shi Houchao Zhang School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China

The focus of this paper is on a linearized backward differential formula(BDF)scheme with Galerkin FEM for the nonlinear Klein-Gordon-Schrödinger equations(KGSEs)with damping *** error estimates and superconvergence results are proved without any time-step restriction condition for the proposed *** proof consists of three ***,a temporal-spatial error splitting argument is employed to bound the numerical solution in certain strong ***,optimal error estimates are derived through a novel splitting technique to deal with the time derivative and some sharp estimates to cope with the nonlinear ***,by virtue of the relationship between the Ritz projection and the interpolation,as well as a so-called"lifting"technique,the superconvergence behavior of order O(h^(2)+τ^(2))in H^(1)-norm for the original variables are ***,a numerical experiment is conducted to confirm our theoretical ***,h is the spatial subdivision parameter,andτis the time step.

关键词： KGSEs with damping mechanism Linearized BDF Galerkin FEM Optimal error estimates Superconvergence

SUPERCONVERGENCE ANALYSIS FOR TIME-FRACTIONAL DIFFUSION EQUATIONS WITH NONCONFORMING MIXED FINITE ELEMENT METHOD

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Journal of Computational Mathematics 2019年第4期37卷 488-505页

作者： Houchao Zhang dongyang shi School of Mathematics and Statistics Pingdingshan University Pingdingshan 467000 China School of Mathematics and Statistics Zhengzhou University Zhengzhou 450001 China

In this paper, a fully discrete scheme based on the LI approximation in temporal direction for the fractional derivative of order in (0,1) and nonconforming mixed finite element method (MFEM) in spatial direction is established. First, we prove a novel result of the consistency error estimate with order O(h^2)of EQ1^rot element (see Lemma 2.3). Then, by using the proved character of EQ1^rot element, we present the superconvergent estimates for the original variable u in the broken H^1-norm and the flux →p =△u in the (L^2)^2-norm under a weaker regularity of the exact solution. Finally, numerical results are provided to confirm the theoretical analysis.

关键词： Nonconforming MFEM LI method Time-fractional diffusion equations Superconvergence

SUPERCONVERGENCE ANALYSIS OF THE STABLE CONFORMING RECTANGULAR MIXED FINITE ELEMENTS FOR THE LINEAR ELASTICITY PROBLEM

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Journal of Computational Mathematics 2014年第2期32卷 205-214页

作者： dongyang shi Minghao Li School of Mathematics and Statistics Zhengzhou University Zhengzhou 450001 China School of Aerospace Engineering and Applied Mechanics Tongji University Shanghai 200092 China

In this paper, we consider the linear elasticity problem based on the Hellinger-Reissner variational principle. An O（h2） order superclose property for the stress and displacement and a global superconvergence result of the displacement are established by employing a Clement interpolation, an integral identity and appropriate postprocessing techniques.

关键词： Elasticity Supercloseness Global superconvergence.