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1引言有限元导数恢复技术是近年来发展起来的计算有限元导数并获得导数逼近超收敛性的一种新的后处理技术.对于一维和二维区域上的二阶椭圆边值问题,文[1,2]提出了Z-Z小片插值技术,得到了有限元导数逼近在小片恢复区域上的一阶超收敛结果和剖分节点处二阶强超收敛性;文[3,4]则建立了更为实用的小片插值恢复技术并得到与文[1,2]相平行的超收敛结果;文[5]对两点边值问题构造了一种积分形式的导数恢复公式,利用这个公式可获得剖分节点处有限元导数逼近的O(h~(2k))阶超收敛估计.本文将对一维四阶椭圆 相似文献
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Superconvergence analysis of the finite element method for nonlinear hyperbolic equations with nonlinear boundary condition 总被引:1,自引:0,他引:1
This paper discusses the semidiscrete finite element method for nonlinear hyperbolic equations with nonlinear boundary condition. The superclose property is derived through interpolation instead of the nonlinear H^1 projection and integral identity technique. Meanwhile, the global superconvergence is obtained based on the interpolated postprocessing techniques. 相似文献
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In this paper, the superconvergence analysis of a two‐grid method (TGM) with low‐order finite elements is presented for the fourth‐order dispersive‐dissipative wave equations for a second order fully discrete scheme. The superclose estimates in the H1‐norm on the two grids are obtained by the combination technique of the interpolation and Ritz projection. Then, with the help of the interpolated postprocessing technique, the global superconvergence properties are deduced. Finally, numerical results are provided to show the performance of the proposed TGM for conforming bilinear element and nonconforming element, respectively. It shows that the TGM is an effective method to the problem considered of our paper compared with the traditional Galerkin finite element method (FEM). 相似文献
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Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one‐dimensional second‐order wave equation
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Mahboub Baccouch 《Numerical Methods for Partial Differential Equations》2015,31(5):1461-1491
In this article, we analyze a residual‐based a posteriori error estimates of the spatial errors for the semidiscrete local discontinuous Galerkin (LDG) method applied to the one‐dimensional second‐order wave equation. These error estimates are computationally simple and are obtained by solving a local steady problem with no boundary condition on each element. We apply the optimal L2 error estimates and the superconvergence results of Part I of this work [Baccouch, Numer Methods Partial Differential Equations 30 (2014), 862–901] to prove that, for smooth solutions, these a posteriori LDG error estimates for the solution and its spatial derivative, at a fixed time, converge to the true spatial errors in the L2‐norm under mesh refinement. The order of convergence is proved to be , when p‐degree piecewise polynomials with are used. As a consequence, we prove that the LDG method combined with the a posteriori error estimation procedure yields both accurate error estimates and superconvergent solutions. Our computational results show higher convergence rate. We further prove that the global effectivity indices, for both the solution and its derivative, in the L2‐norm converge to unity at rate while numerically they exhibit and rates, respectively. Numerical experiments are shown to validate the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1461–1491, 2015 相似文献
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A local parallel superconvergence method for the incompressible flow by coarsening projection
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In this article, we investigate a local parallel superconvergence method by coarsening projection for the incompressible Stokes flow. The method is a combination of the local superconvergence technique and the given framework of local parallel method. For the smooth subdomains, the local superconvergence method is applied in a higher order finite dimensional space corresponding to an appropriate coarse mesh on interior domain. Moreover, a useful and flexible local parallel method is designed to obtain the local parallel superconvergence results of presented method, which offset theoretical limitation of the model without the smoothness of the exact solution and a priori regularity of the underlying problem over the whole domain. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1209–1223, 2015 相似文献
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This paper is a summary of our study on the superconvergence of the finite element solutions and error estimators. We will persent the analysis of %-superconvergence for finite element solutions of the Poisson equation in the interior of meshes of triangles with straight edges, as well as the analysis at the boundary. The %-superconvergence via local averaging will also be presented, and the error estimators are compared in the sense of %-superconvergence. 相似文献
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B. Bialecki G. Fairweather A. Karageorghis Q.N. Nguyen 《BIT Numerical Mathematics》2008,48(3):449-472
We formulate new optimal quadratic spline collocation methods for the solution of various elliptic boundary value problems
in the unit square. These methods are constructed so that the collocation equations can be solved using a matrix decomposition
algorithm. The results of numerical experiments exhibit the expected optimal global accuracy as well as superconvergence phenomena.
AMS subject classification (2000) 65N35, 65N22 相似文献