FINITE VOLUME SUPERCONVERGENCE APPROXIMATION FOR ONE-DIMESIONAL SINGULARLY PERTURBED PROBLEMS  

作　　者：Waixiang Cao Zhimin Zhang Qingsong Zou 

机构地区：[1]School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China [2]Beijing Cornputational Science Research Center, Beijing 100084, ChinaDepartment of Mathematics, Wayne State University, Detroit, MI 48202, USA [3]School of MathemaLics and Computational Science and Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, China

出　　处：《Journal of Computational Mathematics》2013年第5期488-508,共21页计算数学（英文）

摘　　要：We analyze finite volume schemes of arbitrary order r for the one-dimensional singu- larly perturbed convection-diffusion problem on the Shishkin mesh. We show that the error under the energy norm decays as （N-11n（N 4- 1））r, where 2N is the number of subinter- vals of the primal partition. Furthermore, at the nodal points, the error in function value approximation super-converges with order （N-11n（N ＋ 1））2r, while at the Gauss points, the derivative error super-converges with order （N-11n（N ＋ 1））r＋1. All the above conver- gence and superconvergence properties are independent of the perturbation parameter e. Numerical results are presented to support our theoretical findings.We analyze finite volume schemes of arbitrary order r for the one-dimensional singu- larly perturbed convection-diffusion problem on the Shishkin mesh. We show that the error under the energy norm decays as （N-11n（N 4- 1））r, where 2N is the number of subinter- vals of the primal partition. Furthermore, at the nodal points, the error in function value approximation super-converges with order （N-11n（N ＋ 1））2r, while at the Gauss points, the derivative error super-converges with order （N-11n（N ＋ 1））r＋1. All the above conver- gence and superconvergence properties are independent of the perturbation parameter e. Numerical results are presented to support our theoretical findings.

关 键 词：Finite Volume High Order SUPERCONVERGENCE Convection-Diffsuion. 

分 类 号：O241.81[理学—计算数学] O241.82[理学—数学]