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A PRIORI ERROR ESTIMATES FOR LEAST-SQUARES MIXED FINITE ELEMENT APPROXIMATION OF ELLIPTIC OPTIMAL CONTROL PROBLEMS

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Journal of Computational Mathematics 2015年第2期33卷 113-127页

作者： Hongfei hongxing rui College of Science China University of Petroleum Qingdao 266580 China School of Mathematics Shandong University Jinan 250100 China

In this paper, a constrained distributed optimal control problem governed by a first- order elliptic system is considered. Least-squares mixed finite element methods, which are not subject to the Ladyzhenkaya-Babuska-Brezzi consistency condition, are used for solving the elliptic system with two unknown state variables. By adopting the Lagrange multiplier approach, continuous and discrete optimality systems including a primal state equation, an adjoint state equation, and a variational inequality for the optimal control are derived, respectively. Both the discrete state equation and discrete adjoint state equation yield a symmetric and positive definite linear algebraic system. Thus, the popular solvers such as preconditioned conjugate gradient （PCG） and algebraic multi-grid （AMG） can be used for rapid solution. Optimal a priori error estimates are obtained, respectively, for the control function in L2 （Ω）-norm, for the original state and adjoint state in H1 （Ω）-norm, and for the flux state and adjoint flux state in H（div; Ω）-norm. Finally, we use one numerical example to validate the theoretical findings.

关键词： Optimal control Least-squares mixed finite element methods First-order el-liptic system A priori error estimates.

The MFE-CFE-GFE Method for the Fully Coupled Quasi-Static Thermo-Poroelastic Problem

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Numerical Mathematics(Theory,Methods and Applications) 2023年第3期16卷 792-819页

作者： Jing Zhang hongxing rui School of Mathematics Shandong UniversityJinanShandong 250100China

In this work,we consider a combined finite element method for fully coupled nonlinear thermo-poroelastic model *** mixed finite element(MFE)method is used for the pressure,the characteristics finite element(CFE)method is used for the temperature,and the Galerkin finite element(GFE)method is used for the elastic *** semi-discrete and fully discrete finite element schemes are established and the stability of this method is *** derive error estimates for the pressure,temperature and *** numerical examples are presented to confirm the accuracy of the method.

关键词： Quasi-static thermo-poroelasty characteristics finite element method porous media numerical experiments

EXTRAPOLATION METHODS FOR COMPUTING HADAMARD FINITE-PART INTEGRAL ON FINITE INTERVALS

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Journal of Computational Mathematics 2019年第2期37卷 261-277页

作者： Jin Li hongxing rui School of Science Shandong Jianzhu University Jinan 250101 China School of Mathematics Shandong University Jinan 250100 China

In this paper, we presen t the composite rectangle rule for the comp ut at ion of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel l/(x-s)2 and we obtain the asymptotic expansion of error function of the middle rectangle rule. Based on the asymptotic expansion, two extrapolation algorithms are presented and their convergence rates are proved, which are the same as the Euler-Maclaurin expansions of classical middle rec tangle rule approximations. At last, some numerical results are also illustrated to confirm the theoretical results and show the efficiency of the algorithms.

关键词： Hadamard finite-part integral Extrapolation method Composite rectangle rule. Superconvergence Error functional.

BLOCK-CENTERED FINITE DIFFERENCE METHODS FOR NON-FICKIAN FLOW IN POROUS MEDIA

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Journal of Computational Mathematics 2018年第4期36卷 492-516页

作者： Xiaoli Li hongxing rui School of Mathematics Shandong University Jinan Shandong 250100 China

In this article, two block-centered finite difference schemes are introduced and analyzed to solve the parabolic integro-differential equation arising in modeling non-Fickian flow in porous media. One scheme is Euler backward scheme with first order accuracy in time increment while the other is Crank-Nicolson scheme with second order accuracy in time increment. Stability analysis and second-order error estimates in spatial meshsize for both pressure and velocity in discrete L^2 norms are established on non-uniform rectangular grid. Numerical experiments using the schemes show that the convergence rates are in agreement with the theoretical analysis.

关键词： Block-centered finite difference Parabolic integro-differential equation Nonuniform Error estimates Numerical analysis

LEAST-SQUARES GALERKIN PROCEDURE FOR SECOND-ORDER HYPERBOLIC EQUATIONS

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Journal of Systems Science & Complexity 2011年第2期24卷 381-393页

作者： Hui GUO hongxing rui Chao LIN School of Mathematics and Computational Science China University of Petroleum Dongying 257061 China. School of Mathematics and System Science Shandong University Jinan 250100 China. Network and Education Technology Center China University of Petroleum Dongying 257061 China.

This paper proposes the least-squares Galerkin finite dement scheme to solve secona-oraer hyperbolic equations. The convergence analysis shows that the method yields the approximate solutions with optimal accuracy in （L2 （Ω））2 × L2 （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. Key words Convergence analysis, Galerkin finite element, hyperbolic equations, least-squares, nu- merical example.

关键词： Convergence analysis Galerkin finite element hyperbolic equations least-squares nu-merical example.

DOMAIN DECOMPOSITION METHOD FOR PARABOLIC EQUATION ON GENERAL DOMAIN

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Applied Mathematics(A Journal of Chinese Universities) 1995年第1期10卷 25-34页

作者： rui hongxing Department of Mathematics Shandong University Jinan

The nonoverlapping domain decomposition method for parabolic partialdifferential equation on general domain is considered. A kind of domain decompositionthat uses the finite element procedure is given. The problem ove... 详细信息

关键词： 1991 MR Subject Classification 65N15 65N55 65N30

New Energy Analysis of Yee Scheme for Metamaterial Maxwell’s Equations on Non-Uniform Rectangular Meshes

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Advances in Applied Mathematics and Mechanics 2021年第6期13卷 1355-1383页

作者： Xixian Bai hongxing rui School of Mathematics Shandong UniversityJinan 250100ShandongChina

In this paper,several new energy identities of metamaterial Maxwell’s equations with the perfectly electric conducting(PEC)boundary condition are proposed and *** new energy identities are different from the Poynting *** using these new energy identities,it is proved that the Yee scheme on non-uniform rectangular meshes is stable in the discrete L2 and H1 norms when the Courant-Friedrichs-Lewy(CFL)condition is *** experiments in twodimension(2D)and 3D are carried out and confirm our analysis,and the superconvergence in the discrete H1 norm is found.

关键词： Metamaterial Maxwell’s equations Yee scheme non-uniform rectangular meshes,energy identities stability

Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium

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Advances in Applied Mathematics and Mechanics 2022年第6期14卷 1433-1455页

作者： Jing Zhang hongxing rui School of Mathematics Shandong UniversityJinanShandong 250100China

In this paper,a two-grid block-centered finite difference method for the incompressible miscible displacement in porous medium is introduced and analyzed,which is to solve a nonlinear equation on coarse mesh space of size H and a linear equation on fine grid of size *** establish the full discrete two-grid block-centered finite difference scheme on a uniform *** error estimates for the pressure,Darcy velocity,concentration variables are derived,which show that the discrete L2 error is O(Dt+h2+H4).Finally,two numerical examples are provided to demonstrate the effectiveness and accuracy of our algorithm.

关键词： Porous media two phase flow block-centered finite difference two-grid numerical analysis.

Finite Element Approximation of Semilinear Parabolic Optimal Control Problems

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Numerical Mathematics(Theory,Methods and Applications) 2011年第4期4卷 489-504页

作者： Hongfei Fu hongxing rui School of Mathematics and Computational Science China University of PetroleumQingdao266555China School of Mathematics Shandong UniversityJinan 250100China

In this paper,the finite element approximation of a class of semilinear parabolic optimal control problems with pointwise control constraint is *** discretize the state and co-state variables by piecewise linear continuous functions,and the control variable is approximated by piecewise constant functions or piecewise linear discontinuous *** a priori error estimates are derived for both the control and state *** convergence orders are also obtained.

关键词： Finite element approximation semilinear parabolic optimal control pointwise control constraint a priori error estimates