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 bil...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.展开更多
In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as ...In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure. The convergence analysis is presented and optimal error estimates of both broken H^1-norm and L^2-norm for velocity as well as the L^2-norm for the pressure are derived.展开更多
In this paper,nonconforming mixed finite element method is proposed to simulate the wave propagation in metamaterials.The error estimate of the semi-discrete scheme is given by convergence order O(h 2),which is less t...In this paper,nonconforming mixed finite element method is proposed to simulate the wave propagation in metamaterials.The error estimate of the semi-discrete scheme is given by convergence order O(h 2),which is less than 40 percent of the computational costs comparing with the same effect by using Nédélec-Raviart element.A Crank-Nicolson full discrete scheme is also presented with O(τ2+h 2)by traditional discrete formula without using penalty method.Numerical examples of 2D TE,TM cases and a famous re-focusing phenomena are shown to verify our theories.展开更多
A nonconforming H^1-Calerkin mixed finite element method is analyzed for Sobolev equations on anisotropic meshes. The error estimates are obtained without using Ritz-Volterra projection.
基金Supported by the National Natural Science Foundation of China(No.10971203,11271340,11101384)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20094101110006)
文摘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.
基金Supported by the National Natural Science Foundation of China(11271340,116713697)Supported by Henan Natural Science Foundation of China(132300410376)
文摘In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure. The convergence analysis is presented and optimal error estimates of both broken H^1-norm and L^2-norm for velocity as well as the L^2-norm for the pressure are derived.
基金supported by P.R.China NSFC(NO.11471296,11571389,11101384)。
文摘In this paper,nonconforming mixed finite element method is proposed to simulate the wave propagation in metamaterials.The error estimate of the semi-discrete scheme is given by convergence order O(h 2),which is less than 40 percent of the computational costs comparing with the same effect by using Nédélec-Raviart element.A Crank-Nicolson full discrete scheme is also presented with O(τ2+h 2)by traditional discrete formula without using penalty method.Numerical examples of 2D TE,TM cases and a famous re-focusing phenomena are shown to verify our theories.
基金Supported by the National Natural Science Foundation of China(No.10671184).
文摘A nonconforming H^1-Calerkin mixed finite element method is analyzed for Sobolev equations on anisotropic meshes. The error estimates are obtained without using Ritz-Volterra projection.
