A moving collocation method for solving time dependent partial differential equations

Applied Numerical Mathematics

Volumn 20, Issue 1-2, 1996, Pages 101-116

  Huang, Weizhang ^a   Russell, Robert D ^b  

^a UNIVERSITY OF KANSAS   (United States)

^b SIMON FRASER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; GEOMETRY; NUMERICAL METHODS; PROBLEM SOLVING;

BURGERS EQUATION; CUBIC HERMITE COLLOCATION DISCRETIZATION; MOVING COLLOCATION METHOD; MOVING MESH METHOD; SOD SHOCKTUBE PROBLEM; THREE POINT FINITE DIFFERENCE DISCRETIZATION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0030081518     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/0168-9274(95)00119-0     Document Type: Article

References (27)

1. D.C. Arney, R. Biswas and J.E. Flaherty, An adaptive mesh moving and refinement procedure for one-dimensional conservation laws, Appl. Numer. Math. 11 (1993) 259-282.
2. U. Ascher, J. Christiansen and R.D. Russell, Collocation software for boundary value ODEs, ACM Trans. Math. Software 7 (1981) 209-222.
3. 1, Math. Comput. 33 (1979) 435-463.
4. C. Basdevant, M. Deville, P. Haldenwang, J.M. Lacroix, J. Auazzani, R. Peyret, P. Orlandi and A.T. Patera, Spectral and finite difference solutions of the Burgers equation, Comput. & Fluids 14 (1986) 23-41.
5. A. Bayliss and E. Turkel, Mappings and accuracy for Chebyshev pseudo-spectral approximations, J. Comput. Phys. 101 (1992) 349-359.
6. E.R. Benton and G.W. Platzman, A table of solutions of the one-dimensional Burgers equation, Quart. Appl. Math. 30 (1972) 195-212.
7. M. Berzins and P.M. Dew, Chebyshev polynomial software for elliptic-parabolic systems of PDEs, ACM Trans. Math. Software 17 (1991) 178-206.
8. D.S. Dodson, Optimal order approximation by polynomial spline functions, PhD Thesis, Purdue University, Lafayette, IN (1972).
9. E.A. Dorfi and L.O'c. Drury, Simple adaptive grids for 1-D initial value problems, J. Comput. Phys. 69 (1987) 175-195.
10. H.A. Dwyer, R.J. Kee and B.R. Sanders, Adaptive grid method for problems in fluid mechanics and heat transfer, AIAA J. 10 (1980) 1205-1212.
11. H.A. Dwyer and B.R. Sanders, Numerical modeling of unsteady flame propagation, SAND77-8275, Sandia Labs, Livermore, CA (1978).
12. E.N. Houstis, W.F. Mitchell and J.R. Rice, Collocation software for second-order elliptic partial differential equations, ACM Trans. Math. Software 11 (1985) 379-412.
13. W. Huang, Y. Ren and R.D. Russell, Moving mesh partial differential equations (MMPDEs) based on the equidistribution principle, SIAM J. Numer. Anal. 31 (1994) 709-730.
14. W. Huang, Y. Ren and R.D. Russell, Moving mesh methods based on moving mesh partial differential equations, J. Comput. Phys. 113 (1994) 279-290.
15. W. Huang and R.D. Russell, Analysis of moving mesh PDEs with spatial smoothing, SIAM J. Numer. Anal. (to appear).
16. W. Huang and R.D. Russell, MOVCOL: moving collocation software for time dependent partial differential equations, in preparation.
17. J. Lang and A. Walter, A finite element method adaptive in space and time for nonlinear reaction-diffusion systems, IMPACT Comput. Sci. Engrg. 4 (1992) 269-314.
18. N.K. Madsen and R.F. Sincovec, PDECOL: General collocation software for partial differential equations, ACM Trans. Math. Software 5 (1979) 326-351.
19. K. Miller, Moving finite elements II, SIAM J. Numer. Anal. 18 (1981) 1033-1057.
20. K. Miller and R.N. Miller, Moving finite elements I, SIAM. Numer. Anal. 18 (1981) 1019-1032.
21. N. Peters and J. Warnatz, eds., Numerical methods in laminar flame propagation, in: Notes in Numerical Fluid Dynamics 6 (Vieweg, Braunschweig, 1982) 232-260.
22. L.R. Petzold, A description of DASSL: A differential/algebraic system solver, SAND82-8637, Sandia Labs, Livermore, CA (1982).
23. L.R. Petzold, An adaptive moving grid method for one-dimensional systems of PDEs and its numerical solution, in: J.E. Flaherty, P.J. Paslow, M.S. Shephard and J.D. Vasilakis, eds., Adaptive Methods for Partial Differential Equations (SIAM, Philadelphia, PA, 1989) 253-265.
24. G.A. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comput. Phys. 27 (1978) 1-31.
25. J.G. Verwer, J.G. Blom and J.M. Sanz-Serna, An adaptive moving grid method for one-dimensional systems of partial differential equations, J. Comput. Phys. 82 (1989) 454-486.
26. G.B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).
27. P.A. Zegeling and J.G. Blom, An evaluation of the gradient-weighted moving-finite-element method in one space dimension, J. Comput. Phys. 103 (1992) 422-441.