The main contents of this paper are to establish a finite element fully-discrete approximate scheme for multi-term time-fractional mixed sub-diffusion and diffusionwave equation with spatial variable coefficient,which...The main contents of this paper are to establish a finite element fully-discrete approximate scheme for multi-term time-fractional mixed sub-diffusion and diffusionwave equation with spatial variable coefficient,which contains a time-space coupled derivative.The nonconforming EQ^(rot)_(1)element and Raviart-Thomas element are employed for spatial discretization,and L1 time-stepping method combined with the Crank-Nicolson scheme are applied for temporal discretization.Firstly,based on some significant lemmas,the unconditional stability analysis of the fully-discrete scheme is acquired.With the assistance of the interpolation operator I_(h)and projection operator Rh,superclose and convergence results of the variable u in H^(1)-norm and the flux~p=k_(5)(x)ru(x,t)in L^(2)-norm are obtained,respectively.Furthermore,the global superconvergence results are derived by applying the interpolation postprocessing technique.Finally,the availability and accuracy of the theoretical analysis are corroborated by experimental results of numerical examples on anisotropic meshes.展开更多
This paper is concerned with a stabilized approach to low-order mixed finite element methods for the Stokes equations.We will provide a posteriori error analysis for the method.We present two a posteriori error indica...This paper is concerned with a stabilized approach to low-order mixed finite element methods for the Stokes equations.We will provide a posteriori error analysis for the method.We present two a posteriori error indicators which will be demonstrated to be globally upper and locally lower bounds for the error of the finite element discretization.Finally two numerical experiments will be carried out to show the efficiency on constructing adaptive meshes.展开更多
In this paper, the general formulation of anew proposed iteration algorithm of mixed BEM/FEM for eigenvalue problems of elastodynamics is described. Approximate fundamental solutions of elastodynamics are adopted in t...In this paper, the general formulation of anew proposed iteration algorithm of mixed BEM/FEM for eigenvalue problems of elastodynamics is described. Approximate fundamental solutions of elastodynamics are adopted in the normal mixed BEM/FEM equations. The accuracy of solutions is progressively improved by the iteration procedure. Not only could the awkwardness of non-algebraic eigenvalue equations be avoided but also the accuracy of numerical solutions is almost independent of the interior meshing. All these give many advantages in numerical calculation. The algorithm is applied to free torsional vibration analysis of bodies of revolution. A few cases are studied. All of the numerical results are very good.展开更多
A low order nonconforming mixed finite element method(FEM)is established for the fully coupled non-stationary incompressible magnetohydrodynamics(MHD)problem in a bounded domain in 3D.The lowest order finite elements ...A low order nonconforming mixed finite element method(FEM)is established for the fully coupled non-stationary incompressible magnetohydrodynamics(MHD)problem in a bounded domain in 3D.The lowest order finite elements on tetrahedra or hexahedra are chosen to approximate the pressure,the velocity field and the magnetic field,in which the hydrodynamic unknowns are approximated by inf-sup stable finite element pairs and the magnetic field by H^(1)(Ω)-conforming finite elements,respectively.The existence and uniqueness of the approximate solutions are shown.Optimal order error estimates of L^(2)(H^(1))-norm for the velocity field,L^(2)(L^(2))-norm for the pressure and the broken L^(2)(H^(1))-norm for the magnetic field are derived.展开更多
基金The work is supported by the National Natural Science Foundation of China(Nos.11971416 and 11871441)the Scientific Research Innovation Team of Xuchang University(No.2022CXTD002)the Foundation for University Key Young Teacher of Henan Province(No.2019GGJS214).
文摘The main contents of this paper are to establish a finite element fully-discrete approximate scheme for multi-term time-fractional mixed sub-diffusion and diffusionwave equation with spatial variable coefficient,which contains a time-space coupled derivative.The nonconforming EQ^(rot)_(1)element and Raviart-Thomas element are employed for spatial discretization,and L1 time-stepping method combined with the Crank-Nicolson scheme are applied for temporal discretization.Firstly,based on some significant lemmas,the unconditional stability analysis of the fully-discrete scheme is acquired.With the assistance of the interpolation operator I_(h)and projection operator Rh,superclose and convergence results of the variable u in H^(1)-norm and the flux~p=k_(5)(x)ru(x,t)in L^(2)-norm are obtained,respectively.Furthermore,the global superconvergence results are derived by applying the interpolation postprocessing technique.Finally,the availability and accuracy of the theoretical analysis are corroborated by experimental results of numerical examples on anisotropic meshes.
基金supported by the NSF of China(No.10971166)the National Basic Research Program(No.2005CB321703).
文摘This paper is concerned with a stabilized approach to low-order mixed finite element methods for the Stokes equations.We will provide a posteriori error analysis for the method.We present two a posteriori error indicators which will be demonstrated to be globally upper and locally lower bounds for the error of the finite element discretization.Finally two numerical experiments will be carried out to show the efficiency on constructing adaptive meshes.
文摘In this paper, the general formulation of anew proposed iteration algorithm of mixed BEM/FEM for eigenvalue problems of elastodynamics is described. Approximate fundamental solutions of elastodynamics are adopted in the normal mixed BEM/FEM equations. The accuracy of solutions is progressively improved by the iteration procedure. Not only could the awkwardness of non-algebraic eigenvalue equations be avoided but also the accuracy of numerical solutions is almost independent of the interior meshing. All these give many advantages in numerical calculation. The algorithm is applied to free torsional vibration analysis of bodies of revolution. A few cases are studied. All of the numerical results are very good.
基金supported by the National Natural Science Foundations of China(Grant No.12071443)。
文摘A low order nonconforming mixed finite element method(FEM)is established for the fully coupled non-stationary incompressible magnetohydrodynamics(MHD)problem in a bounded domain in 3D.The lowest order finite elements on tetrahedra or hexahedra are chosen to approximate the pressure,the velocity field and the magnetic field,in which the hydrodynamic unknowns are approximated by inf-sup stable finite element pairs and the magnetic field by H^(1)(Ω)-conforming finite elements,respectively.The existence and uniqueness of the approximate solutions are shown.Optimal order error estimates of L^(2)(H^(1))-norm for the velocity field,L^(2)(L^(2))-norm for the pressure and the broken L^(2)(H^(1))-norm for the magnetic field are derived.
