对流扩散方程特征线三角元法的一致估计

利用三角形线性元的积分恒等式,给出了二维非定常对流占优扩散方程的特征线有限元解和真解的一致最优估计,并利用插值后处理算子,得到了有限元解梯度的一致超收敛估计,即只与初值和右端项有关,而与ε无关

对流扩散方程特征线双线性元的一致估计

利用双线性元的积分恒等式,给出了二维非定常对流占优扩散方程的特征线有限元解和真解的一致误差估计,并利用插值后处理算子给出了有限元解梯度的一致超收敛估计,即上述误差与ε无关,而仅与右端f和初值u_0有关

对流扩散方程三角形有限元解的一致估计

利用三角形线性元的积分恒等式,给出了二维非定常对流扩散方程的半离散有限元解和真解的一致最优误差估计,即误差与ε无关,而仅与右端f和初值u_0有关

三维有限元本征值的外推

通过二维和三维积分恒等式,探讨泊松方程本征值问题三角线元和四面体线元Richardson外推的可行性.理论分析表明,如果剖分为均匀一致和拟一致,外推均可将解的精度提高二阶

A posteriori error estimator for eigenvalue problems by mixed finite element method

NSFC; National Natural Science Foundation of China [11001259, 11031006, 11071265, 11201501, 91230110]; National Basic Research Program of China (973 Project) [2011CB309703]; International S&T Cooperation Program of China [2010DFR00700]; Croucher Foundation of Hong Kong Baptist University; National Center for Mathematics and Interdisciplinary Science, CAS; President Foundation of AMSS-CAS; Fundamental Research Funds for the Central Universities [2012121003]In this paper, a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed, based on a type of superconvergence result of the eigenfunction approximation. Its efficiency and reliability are proved by both theoretical analysis and numerical experiments

Uniform error estimates for triangular finite element solutions of advection-diffusion equations

In this paper, the authors use the integral identities of triangular linear elements to prove a uniform optimal-order error estimate for the triangular element solution of two-dimensional time-dependent advection-diffusion equations. Also the authors introduce an interpolation postprocessing operator to get the superconvergence estimate under the epsilon weighted energy norm. The estimates above depend only on the initial and right data but not on the scaling parameter epsilon

Multiple-instance discriminant analysis

Multiple-instance discriminant analysis (MIDA) is proposed to cope with the feature extraction problem in multiple-instance learning. Similar to MidLABS, MIDA is also derived from linear discriminant analysis (LDA), and both algorithms can be treated as multiple-instance extensions of LDA. Different from MidLABS which learns from the bag level, MIDA is designed from the instance level. MIDA consists of two versions, i.e., binary-class MIDA (B-MIDA) and multi-class MIDA (M-MIDA), which are utilized to cope with binary-class (standard) and multi-class multiple-instance learning tasks, respectively. The block coordinate ascent approach, by which we seek positive prototypes (the most positive instance in a positive bag is termed as the positive prototype of this bag) and projection vectors alternatively and iteratively, is proposed to optimize B-MIDA and M-MIDA to obtain lower dimensional transformation subspaces. Extensive experiments empirically demonstrate the effectiveness of B-MIDA and M-MIDA in extracting discriminative components and weakening class-label ambiguities for instances in positive bags. (C) 2014 Elsevier Ltd. All rights reserved