应用数学学报(英文版)
HOME | ABOUT JOURNAL | EDITORIAL BOARD | FOR AUTHORS | SUBSCRIPTIONS | ADVERTISEMENT | CONTACT US
 
Acta Mathematicae Applicatae
Sinica, Chinese Series
 
   
   
Adv Search »  
Acta Mathematicae Applicatae Sinica, English Series 2011, Vol. 27 Issue (3) :495-502    DOI: 10.1007/s10255-011-0086-6
ARTICLES Current Issue | Next Issue | Archive | Adv Search << | >>
A Two-grid Method with Expanded Mixed Element for Nonlinear Reaction-diffusion Equations
Wei Liu1,2, Hong-xing Rui1, Hui Guo3
1. School of Mathematics, Shandong University, Jinan 250100, China;
2. School of Mathematics and Information, Ludong University, Yantai 264025, China;
3. School of Mathematics and Computational Science, China University of Petroleum, Dongying 257061, China
Download: PDF (1KB)   HTML (1KB)   Export: BibTeX or EndNote (RIS)      Supporting Info
Abstract Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model the hydrologic and bio-geochemical phenomena. To linearize the mixed-method equations, we use a two-grid method involving a small nonlinear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates are derived which demonstrate that the error is Ot + hk+1 + H 2k+2-d/2) (k ≥ 1), where k is the degree of the approximating space for the primary variable and d is the spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problems.  
Service
Email this article
Add to my bookshelf
Add to citation manager
Email Alert
RSS
Articles by authors
Keywordstwo-grid method   expanded mixed finite element   reaction-diffusion equation   nonlinear problem     
Abstract: Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model the hydrologic and bio-geochemical phenomena. To linearize the mixed-method equations, we use a two-grid method involving a small nonlinear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates are derived which demonstrate that the error is Ot + hk+1 + H 2k+2-d/2) (k ≥ 1), where k is the degree of the approximating space for the primary variable and d is the spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problems.  
Keywordstwo-grid method,   expanded mixed finite element,   reaction-diffusion equation,   nonlinear problem     
Received: 2008-11-14;
Fund:

Supported by the National Natural Science Foundation of China Grant (No. 10771124); the Research Fund for Doctoral Program of High Education by State Education Ministry of China (No. 20060422006); the Program for Innovative Research Team in Ludong University; the Discipline Construction Fund of Ludong University.

Cite this article:   
.A Two-grid Method with Expanded Mixed Element for Nonlinear Reaction-diffusion Equations[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2011,V27(3): 495-502
URL:  
http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-011-0086-6      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2011/V27/I3/495
 
[1] Arbogast, T., Wheeler, M.F., Yotov, I. Mixed finite elements for elliptic problems with tensor coefficientsas cell-centered finite differences. SIAM J. Numer. Anal., 34: 828-852 (1997)
[2] Chen, Y.P., Huang, Y.Q., Yu, D.H. A two-grid method for expanded mixed finite-element solution ofsemilinear reaction-diffusion equations. International Journal for Numerical Methods in Engineering, 57(2):193-209 (2003)
[3] Chen, Y.P., Liu, H.W., Liu, S. Analysis of two-grid methods for reaction diffusion equations by expandedmixed finite element methods. International Journal for Numerical Methods in Engineering , 69(2): 408-422(2007)
[4] Chen, Z. Expanded mixed element methods for linear second-order elliptic problems (I). RAIRO Model.Math. Anal. Numer., 32: 479-499 (1998)
[5] Chen, Z. Expanded mixed element methods for quasilinear second-order elliptic problems (II). RAIROModel. Math. Anal. Numer., 32: 501-520 (1998)
[6] Dawson, C.N., Wheeler, M.F. Two-grid methods for mixed finite element approximations of nonlinearparabolic equations. Contempt Maths, 180: 191-203 (1994)
[7] He, Y.N., Sun, W.W. Stability and Convergence of the Crank-Nicolson/Adams-Bashforth scheme for theTime-Dependent Navier-Stokes Equations. SIAM J. Numer. Anal., 45(2): 837-869 (2007)
[8] He, Y.N., Sun, W.W. Stabilized finite element methods based on Crank-Nicolson extrapolation scheme forthe time-dependent Navier-Stokes equations. Math. Comp., 76(257): 115-136 (2007)
[9] Huyakorn, P.S., Pinder, G.F. Computational methods in subsurface flow. Academic Press, New York, 1983
[10] Marion, M., Xu, J. Error estimates on a new nonlinear Galerkin method based on two-grid fifite elements.SIAM J. Numer. Anal., 32: 1170-1184 (1995)
[11] Murray, J. Mathematical biology, 2nd Edition. Springer-Verlag, New York, 1993
[12] Woodward, C.S., Dawson, C.N. Analysis of expanded mixed finite element methods for a nonlinear parabolicequation modelling flow into variably saturated porous media. SIAM J. Numer. Anal., 37: 701-724 (2000)
[13] Wu, L., Allen, M.B. A two grid method for mixed element finite solution of reaction-diffusion equations.Numer. Methods for PDE, 15: 317-332 (1999)
[14] Xu, J. A novel two-grid method for semilinear elliptic equations. SIAM J. Sci. Comput., 15: 231-237(1994)
[15] Xu, J. Two-grid discretization techniques for linear and nonlinear PDEs. SIAM J. Numer. Anal., 33:1759-1777 (1996)
没有找到本文相关文献
Copyright 2010 by Acta Mathematicae Applicatae Sinica, English Serie