An adaptive moving mesh method with static rezoning for partial differential equations

Computers and Mathematics with Applications

Volumn 46, Issue 10-11, 2003, Pages 1511-1524

  Hyman, J M ^a   Li, Shengtai ^a,b   Petzold, L R ^b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b University of California   (United States)

Author keywords

Adaptive mesh method; h r method; Initial value problems; Moving mesh; Partial differential equations; Static rezone

Indexed keywords

ALGEBRA; ALGORITHMS; BOUNDARY CONDITIONS; COMPUTER AIDED SOFTWARE ENGINEERING; COMPUTER SIMULATION; ERROR ANALYSIS; FINITE DIFFERENCE METHOD; INITIAL VALUE PROBLEMS; INTEGRATION; LINEAR EQUATIONS;

ADAPTIVE MOVING MESH METHOD; DIFFERENTIAL ALGEBRAIC EQUATION SOLVER; MULTISTEP INTEGRATION METHOD; ONE DIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS; STATIC REZONING;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0346146973     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(03)90187-8     Document Type: Article

References (18)

1. J.G. Verwer, J.G. Blom, R.M. Furzeland and P.A. Zegeling, A moving-grid method for one-dimensional PDEs based on the method of lines, In Adaptive Methods for Partial Differential Equations, (Edited by J.E. Flaherty, P.J. Paslow, M.S. Shephard and J.D. Vasilakis), Society for Industrial and Applied Mathematics, Philadelphia, PA, 1989.
2. W. Z. Huang, Y. Ren, and R.D. Russell, Moving mesh methods based on moving mesh partial differential equations, J. Comput. Phys. 113, 279-290, (1994).
3. J.M. Hyman, Adaptive moving mesh methods for partial differential equations, In Advances in Reactor Computations, pp. 24-43, American Nuclear Society Press, La Grange Park, IL, (1983).
4. J.M. Hyman and B. Larrouturou, Dynamic rezone methods for partial differential equations in one space dimension, Appl. Numer. Math. 5, 435-450, (1989).
5. L.R. Petzold, Observations on an adaptive moving grid method for one-dimensional systems of partial differential equations, Appl. Numer. Math. 3, 347-360, (1987).
6. J.M. Hyman and M.J. Naughton, Static rezone method for tensor product grids, In Lectures in Applied Mathematics, Volume 22, pp. 321-343, American Mathematical Society, (1985).
7. J.E. Flaherty and P.K. Moore, Integrated space-time adaptive hp-refinement methods for parabolic systems, Appl. Numer. Math. 16, 317-341, (1995).
8. A.V. Wouwer, P. Saucez and W. Schieser, Adaptive Method of Lines, CRC Press, (2001).
9. R.M. Furzeland, J.G. Verwer and P.A. Zegeling, A numerical study of three moving grid methods for one-dimensional partial differential equations which are based on the method of lines, J. Comput. Phys. 89, 349-388, (1990).
10. M. Berzins, P.J. Capon and P.K. Jimack, On spatial adaptivity and interpolation when using the method of lines, Appl. Numer. Math. 26, 117-133, (1998).
11. K.E. Brenan, S.L. Campbell and L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Second Edition, SIAM, (1995).
12. S. Adjerid and J.E. Flaherty, A moving-mesh finite element method with local refinement for parabolic partial differential equations, Comput. Meth. in Appl. Mech. Eng. 55, 3-26, (1986).
13. S. Li and L. Petzold, Moving mesh method with upwinding schemes for time-dependent PDEs, J. Comput. Phys. 131, 368-377, (1997).
14. S. Li, Adaptive mesh methods and software for time dependent partial differential equations, Ph.D. Thesis, Department of Computer Science, University of Minnesota, (1998).
15. J.M. Hyman, Accurate monotonicity preserving cubic interpolation, SIAM J. Sci. Stat. Comp. 4, 645-654, (1983).
16. E.A. Dorfi and L.O'c. Drury, Simple adaptive grids for 1-D initial value problems, J. Comput. Phys. 69, 175-195, (1987).
17. S. Adjerid and J.E. Flaherty, A moving finite element method with error estimation and refinement for one-dimensional time dependent partial differential equations, SIAM J. Num. Anal. 23, 778-795 (1986).
18. N.N. Carlson and K. Miller, Design and application of a gradient weighted moving finite element code, Part I, in 1-D., SIAM J. Sci. Comp. 19, 728-765, (1998).