A COUPLED CONTINUOUS-DISCONTINUOUS FEM APPROACH FOR CONVECTION DIFFUSION EQUATIONS

doi:10.1016/S0252-9602(11)60260-9

Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (2): 601-612.doi: 10.1016/S0252-9602(11)60260-9

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A COUPLED CONTINUOUS-DISCONTINUOUS FEM APPROACH FOR CONVECTION DIFFUSION EQUATIONS

ZHU Peng, XIE Zi-Qing, ZHOU Shu-Zi

College of Mathematics and Information Engineering, Jiaxing University, Jiaxing 314001, China Econometrics, Hunan University, Changsha Hunan 410082, China； College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China； College of Mathematics and Econometrics, Hunan University, Changsha 410082, China

Received:2009-07-10 Revised:2009-09-16 Online:2011-03-20 Published:2011-03-20
Supported by:
Supported by National Natural Science Foundation of China (10571046, 10571053, and 10871066), Program for New Century Excellent Talents in University (NCET-06-0712), and Key Laboratory of Computational and Stochastic Mathematics and Its Applications,
Universities of Hunan Province, Hunan Normal University, the Project of Scientific Research Fund of Hunan Provincial Education Department (09K025) and the Key Scientific Research Topic of Jiaxing University (70110X05BL)

Abstract

Abstract:

In this article, we introduce a coupled approach of local discontinuous Galerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. The discontinuous Galerkin method is adopted in the subdomain where the solution varies rapidly, while the standard finite element method is used in the other subdomain due to its lower computational cost. The stability and a priori error estimate are established. We prove that the coupled method has O((ε^1/2}+h^1/2)h^k) convergence rate in an associated norm, where ε is the diffusion coefficient, h is the mesh size and k is the degree of polynomial. The numerical results verify our theoretical results. Moreover, 2k-order superconvergence of the numerical traces at the nodes, and the optimal convergence of the errors under L² norm are observed numerically on the uniform mesh. The numerical results also indicate that the coupled method has the same convergence order and almost the same errors as the purely LDG method.

Key words: Convection diffusion problems, local discontinuous Galerkin method, finite element method, superconvergence

CLC Number:

65N15

ZHU Peng, XIE Zi-Qing, ZHOU Shu-Zi. A COUPLED CONTINUOUS-DISCONTINUOUS FEM APPROACH FOR CONVECTION DIFFUSION EQUATIONS[J].Acta mathematica scientia,Series B, 2011, 31(2): 601-612.

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A COUPLED CONTINUOUS-DISCONTINUOUS FEM APPROACH FOR CONVECTION DIFFUSION EQUATIONS

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