A new mixed finite element method for Burgers’ equation
In this paper, anH 1-Galerkin mixed finite element method is used to approximate the solution as well as the flux of Burgers’ equation. Error estimates have been derived. The results of the numerical experiment show the efficacy of the mixed method and justifies the theoretical results obtained in the paper.
AMS Mathematics Subject Classification65M60 65M15 65M12
Key words and phrasesBurgers’ equation H1-Galerkin mixed method finite element error estimates computer implementation
Unable to display preview. Download preview PDF.
- 3.J. M. Burgers,A Mathematical model illustrating the theory of turbulence, Advances in Applied Mechanics, Academic Press, New York,1 (1948) 171–199.Google Scholar
- 6.S. L. Campbell, K. E. Brenan and L. R. Petzold,Numerical Solution of intial value problems in differential-algebraic equations, American Elsevier Science, New York, 1989.Google Scholar
- 9.J. Douglas Jr., T. F. Dupont and M. F. Wheeler,H 1-Galerkin methods for the Laplace and heat equations, Mathematical Aspect of Finite Elements in Partial Differential Equations, C.de Boor, ed., Academic Press, New York, 1957, 383–415.Google Scholar
- 12.A. K. Pani and R. S. Anderssen,Finite element methods for identification of parameters in parabolic problems, Inverse Problems in Partial Differential Equations, Proc. Centre for Mathematics and its Applications, Vol.31, A. K. Pani and R. S. Anderssen, eds., Australian National University, Canberra, 1992, 208–221.Google Scholar
- 13.V. Thomée and L. B. Wahlbin,On Galerkin methods in semilinear parabolic problems, Siam J. Numer. Anal.12 (1989), 376–389.Google Scholar