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A NUMERICAL STUDY OF UNIFORM SUPERCONVERGENCE OF LDG METHOD FOR SOLVING singularly perturbed problems

Journal of Computational Mathematics 2009年第2期27卷 280-298页

作者： Ziqing Xie Zuozheng Zhang Zhimin Zhang Key Laboratory of Computational and Stochastic Mathematics and Its Applications Universities of Hunan Province Hunan Normal University Changsha 410081 China

In this paper, we consider the local discontinuous Galerkin method （LDG） for solving singularly perturbed convection-diffusion problems in one- and two-dimensional settings. The existence and uniqueness of the LDG solutions are verified. Numerical experiments demonstrate that it seems impossible to obtain uniform superconvergence for numerical fluxes under uniform meshes. Thanks to the implementation of two-type different anisotropic meshes, i.e., the Shishkin and an improved grade meshes, the uniform 2p ＋ i-order superconvergence is observed numerically for both one-dimensional and twodimensional cases.

关键词： singularly perturbed problems Local discontinuous Galerkin method Numerical fluxes Uniform superconvergence

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A NUMERICAL STUDY OF UNIFORM SUPERCONVERGENCE OF LDG METHOD FOR SOLVING singularly perturbed problems

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Journal of Computational Mathematics 2009年第Z1期 280-298页

作者： Ziqing Xie Zuozheng Zhang Zhimin Zhang Key Laboratory of Computational and Stochastic Mathematics and Its Applications,Universities of Hunan Province,Hunan Normal University,Changsha 410081,China

In this paper,we consider the local discontinuous Galerkin method (LDG) for solv-ing singularly perturbed convection-diffusion problems in one- and two-dimensional *** existence and uniqueness of the LDG solutions are *** ex-periments demonstrate that it seems impossible to obtain uniform superconvergence fornumerical fluxes under uniform *** to the implementation of two-type dif-ferent anisotropic meshes,i.e.,the Shishkin and an improved grade meshes,the uniform2p+1-order superconvergence is observed numerically for both one-dimensional and two-dimensional cases.

关键词： singularly perturbed problems Local discontinuous Galerkin method Numerical fluxes Uniform superconvergence

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Uniform Convergence Analysis for singularly perturbed Elliptic problems with Parabolic Layers

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Numerical Mathematics(Theory,Methods and Applications) 2008年第2期1卷 138-149页

作者： Jichun Li Yitung Chen Department of Mathematical Sciences University of Nevada Las Vegas Nevada 89154-4020 USA Department of Mechanical Engineering University of Nevada Las Vegas Nevada 89154-4027 USA

In this paper, using Lin＇s integral identity technique, we prove the optimal uniform convergence θ（Nx^-2ln^2Nx＋Ny^-2ln^2Ny） in the L^2-norm for singularly perturbed problems with parabolic layers. The error estimate is achieved by bilinear finite elements on a Shishkin type mesh. Here Nx and Ny are the number of elements in the x- and y-directions, respectively. Numerical results are provided supporting our theoretical analysis.

关键词： Finite element methods singularly perturbed problems uniformly convergent

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Numerical Method for singularly perturbed Third Order Ordinary Differential Equations of Convection-Diffusion Type

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Numerical Mathematics(Theory,Methods and Applications) 2014年第3期7卷 265-287页

作者： J.Christy Roja A.Tamilselvan Department of Mathematics Bharathidasan UniversityTiruchirappalli–620024TamilnaduIndia

In this paper,we have proposed a numerical method for singularly perturbed Boundary Value problems(SPBVPs)of convection-diffusion type of third order Ordinary Differential Equations(ODEs)in which the SPBVP is reduced into a weakly coupled system of two ODEs subject to suitable initial and boundary *** numerical method combines boundary value technique,asymptotic expansion approximation,shooting method and finite difference *** order to get a numerical solution for the derivative of the solution,the domain is divided into two regions namely inner region and outer *** shooting method is applied to the inner region while standard finite difference scheme(FD)is applied for the outer *** error estimates are derived for the *** efficiency and accuracy are verified through numerical *** method is easy to implement and suitable for parallel computing.

关键词： singularly perturbed problems third order ordinary differential equations boundary value technique asymptotic expansion approximation shooting method finite difference scheme parallel computation

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