IJPAM: Volume 54, No. 1 (2009)

ALTERNATING-DIRECTION FINITE ELEMENT METHOD
FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS

Zhu Hong
Guang Dong Food and Drug Vocational College
Guang Dong, 510520, P.R. CHINA
e-mail: [email protected]


Abstract.We create alternating-direction finite element method for a class of nonlinear evolution equations by using equivalent transformation. The scheme prevents twice cumulating errors by using the common alternating-direction finite element method to approximate $u$ at first, then to approximate $u_{t}$. By using the calculation of tensor product, $H^{1}$-module estimate and the theory and thechniques of prior estimate we get the best $L^{2}$ module error estimate.

Received: March 3, 2009

AMS Subject Classification: 65M06, 65M12, 80M20

Key Words and Phrases: nonlinear evolution equation, alternating direction finite element method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 1