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Superconvergence of a Nonconforming Finite Element Approximation to Viscoelasticity Type Equations on Anisotropic Meshes 总被引:3,自引:0,他引:3
Dongyang Shi Yucheng Peng Shaochun Chen 《高等学校计算数学学报(英文版)》2006,15(4):375-384
The main aim of this paper is to study the approximation to viscoelasticity type equations with a Crouzeix-Raviart type nonconforming finite element on the anisotropic meshes. The superclose property of the exact solution and the optimal error estimate of its derivative with respect to time are derived by using some novel techniques. Moreover, employing a postprocessing technique, the global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is studied. 相似文献
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Stokes问题各向异性网格Q2-P1混合元超收敛分析 总被引:1,自引:0,他引:1
讨论Stokes问题在各向异性冈格下的Q2-P1混合有限元方法,利用积分恒等式技巧得到了与传统方法相同的超逼近性质,同时基于插值后处理的技巧,构造了速度和压力的一对插值后处理算子,并且前者具有备向异性特征,从而导出了整体超收敛结果. 相似文献
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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. 相似文献
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Hadi Minbashian Hojatolah Adibi Mehdi Dehghan 《Numerical Methods for Partial Differential Equations》2017,33(6):2062-2089
This article concerns with incorporating wavelet bases into existing streamline upwind Petrov‐Galerkin (SUPG) methods for the numerical solution of nonlinear hyperbolic conservation laws which are known to develop shock solutions. Here, we utilize an SUPG formulation using continuous Galerkin in space and discontinuous Galerkin in time. The main motivation for such a combination is that these methods have good stability properties thanks to adding diffusion in the direction of streamlines. But they are more expensive than explicit semidiscrete methods as they have to use space‐time formulations. Using wavelet bases we maintain the stability properties of SUPG methods while we reduce the cost of these methods significantly through natural adaptivity of wavelet expansions. In addition, wavelet bases have a hierarchical structure. We use this property to numerically investigate the hierarchical addition of an artificial diffusion for further stabilization in spirit of spectral diffusion. Furthermore, we add the hierarchical diffusion only in the vicinity of discontinuities using the feature of wavelet bases in detection of location of discontinuities. Also, we again use the last feature of the wavelet bases to perform a postprocessing using a denosing technique based on a minimization formulation to reduce Gibbs oscillations near discontinuities while keeping other regions intact. Finally, we show the performance of the proposed combination through some numerical examples including Burgers’, transport, and wave equations as well as systems of shallow water equations.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2062–2089, 2017 相似文献
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Pratibhamoy Das 《Journal of Difference Equations and Applications》2018,24(3):452-477
This paper studies a higher order numerical method for the singularly perturbed parabolic convection-diffusion problems where the diffusion term is multiplied by a small perturbation parameter. In general, the solutions of these type of problems have a boundary layer. Here, we generate a spatial adaptive mesh based on the equidistribution of a positive monitor function. Implicit Euler method is used to discretize the time variable and an upwind scheme is considered in space direction. A higher order convergent solution with respect to space and time is obtained using the postprocessing based extrapolation approach. It is observed that the convergence is independent of perturbation parameter. This technique enhances the order of accuracy from first order uniform convergence to second order uniform convergence in space as well as in time. Comparative study with the existed meshes show the highly effective behavior of the present method. 相似文献
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In this article, we discuss the superconvergence of the interpolated collocation solutions for Hammerstein equations. Applying this new interpolation postprocessing to the collocation approximation xh, we get a higher accuracy approximation I xh, whose convergence order is the same as that of the iterated collocation method. Such an interpolation postprocessing method is much simpler. Also, numerical experiments are shown to demonstrate the efficiency of the interpolation postprocessing method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
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Pengzhan Huang Xiaoling Ma Rena Askar 《Mathematical Methods in the Applied Sciences》2016,39(12):3496-3505
This paper presents a superconvergence result of the stationary natural convection equations. The superconvergence result is obtained by applying a coarse mesh projection for finite element approximation. This projection method is actually a postprocessing procedure that constructs a new approximation based on a high order polynomial on coarse mesh, under some regularity assumption. Finally, numerical experiment is presented for testing, which confirms the theoretic analysis. Copyright © 2015 John Wiley & Sons, Ltd. 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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研究非线性Sobolev方程Galerkin解法的后处理与超收敛.对半离散及全离散格式,证明了当有限元空间次数,r≥2时,有限元解经过后处理,H1-模和L2-模误差估计可分别提高一阶. 相似文献