共查询到20条相似文献,搜索用时 15 毫秒
1.
A characteristic mixed element method for displacement problems of compressible flow in porous media
Danping Yang 《中国科学A辑(英文版)》1998,41(8):820-828
A new characteristic mixed element scheme is formulated to solve numerically displacement problems of compressible fluids
in porous media. A new mixed finite element method is introduced to solve the pressure equation of parabolic type, in which
the mixed element system is symmetric positive definite and the pressure equation is separated from the flux equation. The
modified method of characteristics is used to treat convection-dominated diffusion equations of the concentrations. The convergence
with optimal accuracy is proved under the general condition.
Project supported in part by China State Major Key Project for Basic Researches, Doctoral Station Foundation and TCTPF of
China State Education Commission. 相似文献
2.
Jiansong Zhang Danping Yang 《Numerical Methods for Partial Differential Equations》2009,25(3):622-636
In this article, we establish a new mixed finite element procedure, in which the mixed element system is symmetric positive definite, to solve the second‐order hyperbolic equations. The convergence of the mixed element methods with continuous‐ and discrete‐time scheme is proved. And the corresponding error estimates are given. Finally some numerical results are presented. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
3.
In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ||·||div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes. 相似文献
4.
Yang LIU Hong LI Wei GAO Siriguleng HE Jinfeng WANG 《Frontiers of Mathematics in China》2012,7(4):725-742
A splitting positive definite mixed finite element method is proposed for second-order viscoelasticity wave equation. The proposed procedure can be split into three independent symmetric positive definite integro-differential sub-system and does not need to solve a coupled system of equations. Error estimates are derived for both semidiscrete and fully discrete schemes. The existence and uniqueness for semidiscrete scheme are proved. Finally, a numerical example is provided to illustrate the efficiency of the method. 相似文献
5.
In this paper, we investigate the superconvergence of fully discrete splitting positive definite mixed finite element (MFE) methods for parabolic optimal control problems. For the space discretization, the state and co-state are approximated by the lowest order Raviart–Thomas MFE spaces and the control variable is approximated by piecewise constant functions. The time discretization of the state and co-state are based on finite difference methods. We derive the superconvergence between the projections of exact solutions and numerical solutions or the exact solutions and postprocessing numerical solutions for the control, state and co-state. A numerical example is provided to validate the theoretical results. 相似文献
6.
Fang Wang Yanping Chen Yuelong Tang 《Numerical Methods for Partial Differential Equations》2014,30(1):175-186
In this article, we use a splitting positive definite mixed finite element procedure to solve the second‐order hyperbolic equation. We analyze the superconvergence property of the mixed element methods with discrete‐time approximation for the hyperbolic equation. Some numerical examples are presented to illustrate our theoretical results. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 175–186, 2014 相似文献
7.
FINITE ELEMENT SIMULATIONS FOR COMPRESSIBLE MISCIBLE DISPLACEMENT WITH MOLECULAR DISPERSION IN POROUS MEDIA 总被引:1,自引:0,他引:1
CHENHUANZHEN LIQIAN 《高校应用数学学报(英文版)》1996,11(1):17-32
Abstract. We consider a nonlinear parabolic system describing compressible miscible displacement in a porous medium [5]. Continuous time and discrete time Galerkinmethods are introduced to approximate the solution snd optimal H1 error estimatesare obtained. One contribution of this paper is a demonstration of how moleculaxdispersion can be handled. 相似文献
8.
Ping Wang Ziwen Jiang Zhe Yin Qiang Xu 《Mathematical Methods in the Applied Sciences》2019,42(9):3341-3358
The compressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations: the pressure equation and the concentration equation are parabolic equation. In this article, we present discontinuous finite volume method for the concentration equation and the pressure equation. The optimal order error estimates for pressure and concentration are obtained in a mesh dependent norm. 相似文献
9.
多孔介质中可压缩可混溶驱动问题的有限体积元法 总被引:2,自引:0,他引:2
马克颖 《高校应用数学学报(A辑)》2005,20(2):161-169
有界区域上多孔介质中可压缩可混溶驱动问题由两个非线性抛物型方程耦合而成:压力方程和饱和度方程均是抛物型方程.运用有限体积元法对两个方程进行数值分析,给出了全离散有限体积元格式,并通过详细的理论分析,得到了近似解与原问题真解的最优H^1模误差估计。 相似文献
10.
Yang Liu Hong Li Jinfeng Wang Siriguleng He 《Numerical Methods for Partial Differential Equations》2012,28(2):670-688
Splitting positive definite mixed finite element (SPDMFE) methods are discussed for a class of second‐order pseudo‐hyperbolic equations. Depending on the physical quantities of interest, two methods are proposed. Error estimates are derived for both semidiscrete and fully discrete schemes. The existence and uniqueness for semidiscrete schemes are proved. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 670–688, 2012 相似文献
11.
A combined method consisting of the mixed finite element method for flow and the local discontinuous Galerkin method for transport is introduced for the one-dimensional coupled system of incompressible miscible displacement problem. Optimal error estimates in L∞(0,T;L2) for concentration c,in L2(0,T;L2)for cxand L∞(0,T;L2) for velocity u are derived. The main technical difficulties in the analysis include the treatment of the inter-element jump terms which arise from the discontinuous nature of the numerical method,the nonlinearity,and the coupling of the models. Numerical experiments are performed to verify the theoretical results. Finally,we apply this method to the one-dimensional compressible miscible displacement problem and give the numerical experiments to confirm the efficiency of the scheme. 相似文献
12.
A combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem which includes molecular diffusion and dispersion in porous media is investigated. That is to say, the mixed finite element method with Raviart-Thomas space is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin (SIPG) approximation. Based on projection interpolations and induction hypotheses, a superconvergence estimate is obtained. During the analysis, an extension of the Darcy velocity along the Gauss line is also used in the evaluation of the coefficients in the Galerkin procedure for the concentration. 相似文献
13.
Sarvesh Kumar 《Numerical Methods for Partial Differential Equations》2012,28(4):1354-1381
The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure‐velocity equation and the concentration equation. In this article, we present a mixed finite volume element method for the approximation of pressure‐velocity equation and a discontinuous Galerkin finite volume element method for the concentration equation. A priori error estimates in L∞(L2) are derived for velocity, pressure, and concentration. Numerical results are presented to substantiate the validity of the theoretical results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012 相似文献
14.
Zhe Yin Hongxing Rui Qiang Xu 《Numerical Methods for Partial Differential Equations》2013,29(3):897-915
A nonlinear system of two coupled partial differential equations models miscible displacement of one incompressible fluid by another in a porous medium. A sequential implicit time‐stepping procedure is defined, in which the pressure and Darcy velocity of the mixture are approximated by a mixed finite element method and the concentration is approximated by a combination of a modified symmetric finite volume element method and the method of characteristics. Optimal order convergence in H1 and in L2 are proved for full discrete schemes. Finally, some numerical experiments are presented. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
15.
Jiansong
Zhang Huiran Han Hui Guo Xiaomang Shen 《Numerical Methods for Partial Differential Equations》2020,36(6):1629-1647
In this article, we propose a combined hybrid discontinuous mixed finite element method for miscible displacement problem with local discontinuous Galerkin method. Here, to obtain more accurate approximation and deal with the discontinuous case, we use the hybrid mixed element method to approximate the pressure and velocity, and use the local discontinuous Galerkin finite element method for the concentration. Compared with other combined methods, this method can improve the efficiency of computation, deal with the discontinuous problem well and keep local mass balance. We study the convergence of this method and give the corresponding optimal error estimates in L∞(L2) for velocity and concentration and the super convergence in L∞(H1) for pressure. Finally, we also present some numerical examples to confirm our theoretical analysis. 相似文献
16.
Jiming Yang Yanping Chen Zhiguang Xiong 《Numerical Methods for Partial Differential Equations》2013,29(6):1801-1820
An efficient time‐stepping procedure is investigated for a two‐dimensional compressible miscible displacement problem in porous media in which the mixed finite element method with Raviart‐Thomas space is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin approximation on Cartesian meshes. Based on the projection interpolations and the induction hypotheses, a superconvergence error estimate is obtained. During the analysis, an extension of the Darcy velocity along the Gauss line is also used in the evaluation of the coefficients in the Galerkin procedure for the concentration. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
17.
A combined method consisting of mixed finite element method (MFEM) for the pressure equation and expanded mixed finite element method with characteristics(CEMFEM) for the concentration equation is presented to solve the coupled system of incompressible miscible displacement problem. To solve the resulting nonlinear system of equations efficiently, the two‐grid algorithm relegates all of the Newton‐like iterations to grids much coarser than the original one, with no loss in order of accuracy. It is shown that coarse space can be extremely coarse and our algorithm achieve asymptotically optimal approximation when the mesh sizes satisfy . Numerical experiment is provided to confirm our theoretical results. 相似文献
18.
Catherine Choquet 《Journal of Mathematical Analysis and Applications》2008,339(2):1112-1133
We study a model describing a compressible and miscible displacement in a porous medium. It consists of a coupled system of nonlinear parabolic partial differential equations. Using nonclassical estimates and renormalization tools, we prove the existence of relevant weak solutions for the problem. This is the first existence result obtained for a transport model containing both the coupling due to the compressibility assumption and the coupling due to the concentration dependent viscosity. 相似文献
19.
Alf Gerisch David F. Griffiths Rüdiger Weiner Mark A. J. Chaplain 《Numerical Methods for Partial Differential Equations》2001,17(2):152-168
In this article we present a method of lines approach to the numerical solution of a system of coupled hyperbolic—parabolic partial differential equations (PDEs). Special attention is paid to preserving the positivity of the solution of the PDEs when this solution is approximated numerically. This is achieved by using a flux‐limited spatial discretization for the hyperbolic equation. We use splitting techniques for the solution of the resulting large system of stiff ordinary differential equations. The performance of the approach applied to a biomathematical model is compared with the performance of standard methods. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 152–168, 2001 相似文献
20.
Aijie Cheng Kaixin Wang Hong Wang 《Numerical Methods for Partial Differential Equations》2012,28(4):1382-1398
A time‐stepping procedure is established and analyzed for the problem of miscible displacement in porous medium. The fluid velocity based on mixed element method is post‐processed by interpolation along Gauss lines. Error analysis shows that this procedure has a superconvergence error bound O(h) with respect to the parameter hp, which is one order higher than the conventional Galerkin or mixed finite element procedures. Compared with the results in the references, the parameter constraint conditions in this article are obviously relaxed. © 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012 相似文献