Abstract
In this paper, H1-Galerkin mixed element method is proposed to simulate the nonlinear Parabolic problem. The problem is considered in one dimensional space. and optimal error estimates are also established. In particular, our methods can simultaneously approximate the scalar unknown and the vector flux effectively, without requiring the LBB consistency condition.
Publisher
Trans Tech Publications, Ltd.
Reference9 articles.
1. Douglas, J, Jr., Dupont, T. F., Wheeler, H1-Galerkin methods for the Laplace and heat equations. Mathematical aspect of finite elements in partialdifferential equation, New York: Academic Press, (1975), 383-415.
2. A. K. Pani and P. C. Das, An H1-Galerkin method for quasilinear parabolic differential equations , in: C.A. Micchelli, D.V. Pai, B. V. Limaya (Eds. ), Methods of Functional Analysis in Approximation Theory ISNM 76, Berkhauser-Verlag, Basel, 357-370, (1986).
3. Pani A K. An H1- Galerkin mixed finite element method for parabolic difference equations, SIAM J. Nmer. Anal., 35(1998): 712-727.
4. B. Fraeijs de Veubeke, Displacement and equilibrium models in the finite element method. Stress Analysis, edited by 0. C. Zienkiewics and G. S. Holister ( Eds. ), Stress Analysis [C], JohnWiley and Sons Ltd., London., 145-197, (1965).
5. K. Hellan, An analysis of elastic plates in flexure by a simplified finite element method, Acta Polytech. Scand. Ci. Ser., v. 46, (1967).