{"title":"A New Time Discontinuous Expanded Mixed Element Method for Convection-dominated Diffusion Equation","authors":"Jinfeng Wang, Yuanhong Bi, Hong Li, Yang Liu, Meng Zhao","volume":60,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":2140,"pagesEnd":2145,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9513","abstract":"
In this paper, a new time discontinuous expanded mixed finite element method is proposed and analyzed for two-order convection-dominated diffusion problem. The proofs of the stability of the proposed scheme and the uniqueness of the discrete solution are given. Moreover, the error estimates of the scalar unknown, its gradient and its flux in the L1( ¯ J,L2( )-norm are obtained.<\/p>\r\n","references":"[1] J.Jr. Douglas, T.F. Russell. Numerical methods for convection-dominated\r\ndiffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal. 19: 871-885.\r\n[2] A. Ware. A spectral Lagrange-Galerkin method for convectiondominated\r\ndiffusion problems, Computer Methods in Applied Mechanics\r\nand Engineering 1994, 116: 227-234.\r\n[3] H.Z. Chen. 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An optimal error estimates of HI- -Galerkin expanded mixed finite element methods for nonlinear viscoelasticity-type equation, Mathematical Problems in Engineering, Volume 2011, Article ID 570980, 18 pages. doi:10.1155\/2011\/570980.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 60, 2011"}