We consider a nonlinear parabolic system describing compressible miscibledisplacement in a porous medium [5]. Continuous time and discrete time Galerkinmethods are introduced to approximate the solution and optimal H^...We consider a nonlinear parabolic system describing compressible miscibledisplacement in a porous medium [5]. Continuous time and discrete time Galerkinmethods are introduced to approximate the solution and optimal H^1 error estimatesare obtained. One contribution of this paper is a demonstration of how moleculardispersion can be handled.展开更多
In this paper, the numerical approximation by Galerkin method for completely compressible miscible displacement with molecular diffusion and dispersion in porous media is considered. Continuous time procedure is intro...In this paper, the numerical approximation by Galerkin method for completely compressible miscible displacement with molecular diffusion and dispersion in porous media is considered. Continuous time procedure is introduced and analysed. Some new techniques are applied to the analysis. Optimal error estimates in L ∞(J;H 1(Ω)) are proved, which implies an essential improvement to existed results. MR Subject Classification: 65N15,65N30.展开更多
Abstract A system of quasilinear coupled equations which arise from simulation of contamination of geologic nulear waste in porous media is studied. We’ll discuss Galerkin method for the model of compressible flow wi...Abstract A system of quasilinear coupled equations which arise from simulation of contamination of geologic nulear waste in porous media is studied. We’ll discuss Galerkin method for the model of compressible flow with molecular diffusion and dispersion. Some new techniques are introcued to error analysis. Only one dimensional case is considered. The optimal error estimate in both L^2 and H^1 is proved. A contribution of this paper is how the dispersion term can be handled,展开更多
Compressible miscible displacement of one fluid by another in porous media is modelled by a nonlinear parabolic system. A finite element procedure is introduced to approximate the concentration of one fluid and the pr...Compressible miscible displacement of one fluid by another in porous media is modelled by a nonlinear parabolic system. A finite element procedure is introduced to approximate the concentration of one fluid and the pressure of the mixture. The concentration is treated by a Galerkin method while the pressure is treated by a parabolic mixed finite element method. The effect of dispersion, which is neglected in [1], is considered. Optimal order estimates in L2 are derived for the errors in the approximate solutions.展开更多
We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpol...We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpolation operator ink is introduced.With the help of ink(not elliptic projection),the optimal error estimate in L∞(J;L2(Ω)) norm of FEM is proved.展开更多
Akind of compressiblemiscible displacement problemswhich includemolecular diffusion and dispersion in porous media are investigated.The mixed finite element method is applied to the flow equation,and the transport one...Akind of compressiblemiscible displacement problemswhich includemolecular diffusion and dispersion in porous media are investigated.The mixed finite element method is applied to the flow equation,and the transport one is solved by the symmetric interior penalty discontinuous Galerkin method.Based on a duality argument,employing projection estimates and approximation properties,a posteriori residual-type hp error estimates for the coupled system are presented,which is often used for guiding adaptivity.Comparing with the error analysis carried out by Yang(Int.J.Numer.Meth.Fluids,65(7)(2011),pp.781-797),the current work is more complicated and challenging.展开更多
基金The work is supported by Science Foundation of the Educational Committee of Shandong Province.
文摘We consider a nonlinear parabolic system describing compressible miscibledisplacement in a porous medium [5]. Continuous time and discrete time Galerkinmethods are introduced to approximate the solution and optimal H^1 error estimatesare obtained. One contribution of this paper is a demonstration of how moleculardispersion can be handled.
文摘In this paper, the numerical approximation by Galerkin method for completely compressible miscible displacement with molecular diffusion and dispersion in porous media is considered. Continuous time procedure is introduced and analysed. Some new techniques are applied to the analysis. Optimal error estimates in L ∞(J;H 1(Ω)) are proved, which implies an essential improvement to existed results. MR Subject Classification: 65N15,65N30.
基金This work is suported by National Science Foundation
文摘Abstract A system of quasilinear coupled equations which arise from simulation of contamination of geologic nulear waste in porous media is studied. We’ll discuss Galerkin method for the model of compressible flow with molecular diffusion and dispersion. Some new techniques are introcued to error analysis. Only one dimensional case is considered. The optimal error estimate in both L^2 and H^1 is proved. A contribution of this paper is how the dispersion term can be handled,
文摘Compressible miscible displacement of one fluid by another in porous media is modelled by a nonlinear parabolic system. A finite element procedure is introduced to approximate the concentration of one fluid and the pressure of the mixture. The concentration is treated by a Galerkin method while the pressure is treated by a parabolic mixed finite element method. The effect of dispersion, which is neglected in [1], is considered. Optimal order estimates in L2 are derived for the errors in the approximate solutions.
基金This research is supported by the Foundation for Talents for Next Century of Shandong University
文摘We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpolation operator ink is introduced.With the help of ink(not elliptic projection),the optimal error estimate in L∞(J;L2(Ω)) norm of FEM is proved.
基金This work was supported by Hunan Provincial Natural Science Foundation of China,Scientific Research Fund ofHunan Provincial Education Department(Grant No.11B032),the Planned Science and Technology Project of Hunan Province(Grant No.2011FJ4146)Aid program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province.The authors cordially thank the referees for their careful reading and helpful comments.
文摘Akind of compressiblemiscible displacement problemswhich includemolecular diffusion and dispersion in porous media are investigated.The mixed finite element method is applied to the flow equation,and the transport one is solved by the symmetric interior penalty discontinuous Galerkin method.Based on a duality argument,employing projection estimates and approximation properties,a posteriori residual-type hp error estimates for the coupled system are presented,which is often used for guiding adaptivity.Comparing with the error analysis carried out by Yang(Int.J.Numer.Meth.Fluids,65(7)(2011),pp.781-797),the current work is more complicated and challenging.
