In this paper, a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for two-point boundary value problems. The key idea is to postprocess the Galerkin approximation, and the analysis sh...In this paper, a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for two-point boundary value problems. The key idea is to postprocess the Galerkin approximation, and the analysis shows that the postproeess improves the order of convergence. Consequently, we obtain asymptotically exact aposteriori error estimators based on the postprocessing results. Numerical examples are included to illustrate the theoretical analysis.展开更多
This paper studies variational discretization for the optimal control problem governed by parabolic equations with control constraints. First of all, the authors derive a priori error estimates where｜｜｜u - Uh｜｜｜...This paper studies variational discretization for the optimal control problem governed by parabolic equations with control constraints. First of all, the authors derive a priori error estimates where｜｜｜u - Uh｜｜｜L∞（J;L2（Ω）） = O（h2 ＋ k）. It is much better than a priori error estimates of standard finite element and backward Euler method where ｜｜｜u- Uh｜｜｜L∞（J;L2（Ω）） = O（h ＋ k）. Secondly, the authors obtain a posteriori error estimates of residual type. Finally, the authors present some numerical algorithms for the optimal control problem and do some numerical experiments to illustrate their theoretical results.展开更多
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 superconvergenc...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.展开更多
基金supported partially by the innovation fund of Shanghai Normal Universitysupported partially by NSERC of Canada under Grant OGP0046726.
文摘In this paper, a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for two-point boundary value problems. The key idea is to postprocess the Galerkin approximation, and the analysis shows that the postproeess improves the order of convergence. Consequently, we obtain asymptotically exact aposteriori error estimators based on the postprocessing results. Numerical examples are included to illustrate the theoretical analysis.
基金supported by National Science Foundation of ChinaFoundation for Talent Introduction of Guangdong Provincial University+2 种基金Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008)Specialized Research Fund for the Doctoral Program of Higher Education(20114407110009)Hunan Provincial Innovation Foundation for Postgraduate under Grant(1x2009B120)
文摘This paper studies variational discretization for the optimal control problem governed by parabolic equations with control constraints. First of all, the authors derive a priori error estimates where｜｜｜u - Uh｜｜｜L∞（J;L2（Ω）） = O（h2 ＋ k）. It is much better than a priori error estimates of standard finite element and backward Euler method where ｜｜｜u- Uh｜｜｜L∞（J;L2（Ω）） = O（h ＋ k）. Secondly, the authors obtain a posteriori error estimates of residual type. Finally, the authors present some numerical algorithms for the optimal control problem and do some numerical experiments to illustrate their theoretical results.
基金supported by National Natural Science Foundation of China(Grant Nos.11001259,11031006,11071265,11201501 and 91230110)National Basic Research Program of China(973 Project)(Grant No. 2011CB309703)+3 种基金International S&T Cooperation Program of China(Grant No. 2010DFR00700)Croucher Foundation of Hong Kong Baptist Universitythe National Center for Mathematics and Interdisciplinary Science,CAS,the President Foundation of AMSS-CASthe Fundamental Research Funds for the CentralUniversities(Grant No. 2012121003)
文摘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.
