In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc...In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.展开更多
This paper proposes a new nonconforming finite difference streamline diffusion method to solve incompressible time-dependent Navier-Stokes equations with a high Reynolds number. The backwards difference in time and th...This paper proposes a new nonconforming finite difference streamline diffusion method to solve incompressible time-dependent Navier-Stokes equations with a high Reynolds number. The backwards difference in time and the Crouzeix-Raviart （CR） element combined with the P0 element in space are used. The result shows that this scheme has good stabilities and error estimates independent of the viscosity coefficient.展开更多
This paper is devoted to studying the superconvergence of streamline diffusion finite element methods for convection-diffusion problems. In [8], under the condition that ε ≤ h^2 the optimal finite element error esti...This paper is devoted to studying the superconvergence of streamline diffusion finite element methods for convection-diffusion problems. In [8], under the condition that ε ≤ h^2 the optimal finite element error estimate was obtained in L^2-norm. In the present paper, however, the same error estimate result is gained under the weaker condition that ε≤h.展开更多
This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary condi...This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary conditions. To overcome such singularities arising from these critical regions, the adaptive finite element method is employed. This scheme is based on the streamline diffusion method combined with Neumann-type posteriori estimator. The effectiveness of this approach is illustrated by different examples with several numerical experiments.展开更多
In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
Multiple fractured horizontal well(MFHW) is widely applied in the development of shale gas. To investigate the gas flow characteristics in shale, based on a new dual mechanism triple continuum model, an analytical sol...Multiple fractured horizontal well(MFHW) is widely applied in the development of shale gas. To investigate the gas flow characteristics in shale, based on a new dual mechanism triple continuum model, an analytical solution for MFHW surrounded by stimulated reservoir volume(SRV) was presented. Pressure and pressure derivative curves were used to identify the characteristics of flow regimes in shale. Blasingame type curves were established to evaluate the effects of sensitive parameters on rate decline curves, which indicates that the whole flow regimes could be divided into transient flow, feeding flow, and pseudo steady state flow. In feeding flow regime, the production of gas well is gradually fed by adsorbed gases in sub matrix, and free gases in matrix. The proportion of different gas sources to well production is determined by such parameters as storability ratios of triple continuum, transmissibility coefficients controlled by dual flow mechanism and fracture conductivity.展开更多
Computational models provide additional tools for studying the brain,however,many techniques are currently disconnected from each other.There is a need for new computational approaches that span the range of physics o...Computational models provide additional tools for studying the brain,however,many techniques are currently disconnected from each other.There is a need for new computational approaches that span the range of physics operating in the brain.In this review paper,we offer some new perspectives on how the embedded element method can fill this gap and has the potential to connect a myriad of modeling genre.The embedded element method is a mesh superposition technique used within finite element analysis.This method allows for the incorporation of axonal fiber tracts to be explicitly represented.Here,we explore the use of the approach beyond its original goal of predicting axonal strain in brain injury.We explore the potential application of the embedded element method in areas of electrophysiology,neurodegeneration,neuropharmacology and mechanobiology.We conclude that this method has the potential to provide us with an integrated computational framework that can assist in developing improved diagnostic tools and regeneration technologies.展开更多
基金supported by the National Basic Research Program under the Grant 2005CB321701the National Natural Science Foundation of China under the Grants 60474027 and 10771211.
文摘In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.
基金supported by the National Natural Science Foundation of China(Nos.11271273 and 11271298)
文摘This paper proposes a new nonconforming finite difference streamline diffusion method to solve incompressible time-dependent Navier-Stokes equations with a high Reynolds number. The backwards difference in time and the Crouzeix-Raviart （CR） element combined with the P0 element in space are used. The result shows that this scheme has good stabilities and error estimates independent of the viscosity coefficient.
基金Supported by the National Natural Science Foundation of China(10471103)
文摘This paper is devoted to studying the superconvergence of streamline diffusion finite element methods for convection-diffusion problems. In [8], under the condition that ε ≤ h^2 the optimal finite element error estimate was obtained in L^2-norm. In the present paper, however, the same error estimate result is gained under the weaker condition that ε≤h.
文摘This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary conditions. To overcome such singularities arising from these critical regions, the adaptive finite element method is employed. This scheme is based on the streamline diffusion method combined with Neumann-type posteriori estimator. The effectiveness of this approach is illustrated by different examples with several numerical experiments.
文摘In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
基金Project(2011ZX05015)supported by Important National Science and Technology Specific Projects of the "Twelfth Five-years" Plan Period,China
文摘Multiple fractured horizontal well(MFHW) is widely applied in the development of shale gas. To investigate the gas flow characteristics in shale, based on a new dual mechanism triple continuum model, an analytical solution for MFHW surrounded by stimulated reservoir volume(SRV) was presented. Pressure and pressure derivative curves were used to identify the characteristics of flow regimes in shale. Blasingame type curves were established to evaluate the effects of sensitive parameters on rate decline curves, which indicates that the whole flow regimes could be divided into transient flow, feeding flow, and pseudo steady state flow. In feeding flow regime, the production of gas well is gradually fed by adsorbed gases in sub matrix, and free gases in matrix. The proportion of different gas sources to well production is determined by such parameters as storability ratios of triple continuum, transmissibility coefficients controlled by dual flow mechanism and fracture conductivity.
基金support provided by Computational Fluid Dynamics Research Corporation(CFDRC)under a sub-contract funded by the Department of Defense,Department of Health Program through contract W81XWH-14-C-0045
文摘Computational models provide additional tools for studying the brain,however,many techniques are currently disconnected from each other.There is a need for new computational approaches that span the range of physics operating in the brain.In this review paper,we offer some new perspectives on how the embedded element method can fill this gap and has the potential to connect a myriad of modeling genre.The embedded element method is a mesh superposition technique used within finite element analysis.This method allows for the incorporation of axonal fiber tracts to be explicitly represented.Here,we explore the use of the approach beyond its original goal of predicting axonal strain in brain injury.We explore the potential application of the embedded element method in areas of electrophysiology,neurodegeneration,neuropharmacology and mechanobiology.We conclude that this method has the potential to provide us with an integrated computational framework that can assist in developing improved diagnostic tools and regeneration technologies.
