An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same t...An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.展开更多
A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements f...A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa- tions. The existence and uniqueness of the solution and the optimal error estimates are proved.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
Using the standard mixed Galerkin methods with equal order elements to solve Biot’s consolidation problems,the pressure close to the initial time produces large non-physical oscillations.In this paper,we propose a cl...Using the standard mixed Galerkin methods with equal order elements to solve Biot’s consolidation problems,the pressure close to the initial time produces large non-physical oscillations.In this paper,we propose a class of fully discrete stabilized methods using equal order elements to reduce the effects of non-physical oscillations.Optimal error estimates for the approximation of displacements and pressure at every time level are obtained,which are valid even close to the initial time.Numerical experiments illustrate and confirm our theoretical analysis.展开更多
This paper presents limits for stability of projection type schemes when using high order pressure-velocity pairs of same degree.Two high order h/p variational methods encompassing continuous and discontinuous Galerki...This paper presents limits for stability of projection type schemes when using high order pressure-velocity pairs of same degree.Two high order h/p variational methods encompassing continuous and discontinuous Galerkin formulations are used to explain previously observed lower limits on the time step for projection type schemes to be stable[18],when h-or p-refinement strategies are considered.In addition,the analysis included in this work shows that these stability limits do not depend only on the time step but on the product of the latter and the kinematic viscosity,which is of particular importance in the study of high Reynolds number flows.We show that high order methods prove advantageous in stabilising the simulations when small time steps and low kinematic viscosities are used.Drawing upon this analysis,we demonstrate how the effects of this instability can be reduced in the discontinuous scheme by introducing a stabilisation term into the global system.Finally,we show that these lower limits are compatible with CourantFriedrichs-Lewy(CFL)type restrictions,given that a sufficiently high polynomial order or a mall enough mesh spacing is selected.展开更多
基金Supported by the National Natural Science Foundation of China (10601022)Natural Science Foundation of Inner Mongolia Autonomous Region (200607010106)Youth Science Foundation of Inner Mongolia University(ND0702)
文摘An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.
基金supported by the National Natural Science Foundation of China(Nos.11271273 and 11271298)
文摘A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa- tions. The existence and uniqueness of the solution and the optimal error estimates are proved.
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The computations in Section 4.4 were done by Free Fem++[21]This research was supported by the Natural Science Foundation of China(No.11271273).
文摘Using the standard mixed Galerkin methods with equal order elements to solve Biot’s consolidation problems,the pressure close to the initial time produces large non-physical oscillations.In this paper,we propose a class of fully discrete stabilized methods using equal order elements to reduce the effects of non-physical oscillations.Optimal error estimates for the approximation of displacements and pressure at every time level are obtained,which are valid even close to the initial time.Numerical experiments illustrate and confirm our theoretical analysis.
基金In addition,EF and SS would like to thank the support of the European Commission for the financial support of the ANADE project under grant contract PITN-GA-289428.
文摘This paper presents limits for stability of projection type schemes when using high order pressure-velocity pairs of same degree.Two high order h/p variational methods encompassing continuous and discontinuous Galerkin formulations are used to explain previously observed lower limits on the time step for projection type schemes to be stable[18],when h-or p-refinement strategies are considered.In addition,the analysis included in this work shows that these stability limits do not depend only on the time step but on the product of the latter and the kinematic viscosity,which is of particular importance in the study of high Reynolds number flows.We show that high order methods prove advantageous in stabilising the simulations when small time steps and low kinematic viscosities are used.Drawing upon this analysis,we demonstrate how the effects of this instability can be reduced in the discontinuous scheme by introducing a stabilisation term into the global system.Finally,we show that these lower limits are compatible with CourantFriedrichs-Lewy(CFL)type restrictions,given that a sufficiently high polynomial order or a mall enough mesh spacing is selected.
