This paper discusses the k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations. When k is even, the averaging numerical flux （the average of left an...This paper discusses the k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations. When k is even, the averaging numerical flux （the average of left and right limits for the discontinuous finite element at nodes） has the optimal-order ultraconvergence 2k ＋ 2. For nanlinear Hamiltonian systems （e.g., SchrSdinger equation and Kepler system） with momentum conservation, the discontinuous finite element methods preserve momentum at nodes. These properties are confirmed by numerical experiments.展开更多
In this paper the ultra convergence of the derivative for odd-degree rectangular elements is addressed. A new, discrete least-squares patch recovery technique is proposed to postprocess the solution derivatives. Such ...In this paper the ultra convergence of the derivative for odd-degree rectangular elements is addressed. A new, discrete least-squares patch recovery technique is proposed to postprocess the solution derivatives. Such recovered derivatives are shown to possess ultra convergence by using projection type interpolation.展开更多
The classical eigenvalue problem of the second-order elliptic operator is approxlmateo with hi-quadratic finite element in this paper. We construct a new superconvergent function recovery operator, from which the O（...The classical eigenvalue problem of the second-order elliptic operator is approxlmateo with hi-quadratic finite element in this paper. We construct a new superconvergent function recovery operator, from which the O（h^8｜ in h｜^2） ultraconvergence of eigenvalue approximation is obtained. Numerical experiments verify the theoretical results.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10771063)
文摘This paper discusses the k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations. When k is even, the averaging numerical flux （the average of left and right limits for the discontinuous finite element at nodes） has the optimal-order ultraconvergence 2k ＋ 2. For nanlinear Hamiltonian systems （e.g., SchrSdinger equation and Kepler system） with momentum conservation, the discontinuous finite element methods preserve momentum at nodes. These properties are confirmed by numerical experiments.
文摘In this paper the ultra convergence of the derivative for odd-degree rectangular elements is addressed. A new, discrete least-squares patch recovery technique is proposed to postprocess the solution derivatives. Such recovered derivatives are shown to possess ultra convergence by using projection type interpolation.
文摘The classical eigenvalue problem of the second-order elliptic operator is approxlmateo with hi-quadratic finite element in this paper. We construct a new superconvergent function recovery operator, from which the O（h^8｜ in h｜^2） ultraconvergence of eigenvalue approximation is obtained. Numerical experiments verify the theoretical results.
