Abstract
An alternating direction finite element scheme for a class of moving boundary problems is studied. Using coordinate transformations of the spatial variants, a new domain independent of the time is obtained and an ADFE scheme on the new domain is proposed. Then the unique solvability of the approximation scheme is proved, and optimal H 1 and L 2 norm space estimates and O((Δt)2) estimate for the temporal variant are obtained.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Zhao, Y., Forhad, A.: A general method for simulation of fluid flows with moving and compliant boundaries on unstructured grids. Computer Methods in Applied Mechanics and Engineering 192, 4439–4466 (2003)
Cui, X.: The finite element methods for the parabolic integro-differential equation in 2-dimensional time-dependent domain. Numerical Mathematics, A Journal of Chinese Universities 21, 228–235 (1999)
Douglas, J., Dupont, T.: Alternating-direction galerkin methods on rectangles. In: Hubbard, B. (ed.) Proceedings of Symposium on Numerical Solution of Partial Differential Equation II, pp. 133–214 (1971)
Cui, X.: Adfe method with high accuracy for nonlinear parabolic integro-differential system with nonlinear boundary conditions. Acta Mathematica Scientia 22B, 473–483 (2002)
Lesaint, P., Touzani, R.: Approximation of the heat equation in a variable domain with application to the stefan problem. SIAM Journal on Numerical Analysis 26, 366–379 (1989)
Ciarlet, P.: The Finite Element Method for Elliptic Problems. North-Holland Publishing Company, Amsterdam (1978)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, XZ., Cui, X., Yong, JH., Sun, JG. (2004). Alternating Direction Finite Element Method for a Class of Moving Boundary Problems. In: Zhang, J., He, JH., Fu, Y. (eds) Computational and Information Science. CIS 2004. Lecture Notes in Computer Science, vol 3314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30497-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-30497-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24127-0
Online ISBN: 978-3-540-30497-5
eBook Packages: Computer ScienceComputer Science (R0)