On spatial adaptivity and interpolation when using the method of lines

Applied Numerical Mathematics

Volumn 26, Issue 1-2, 1998, Pages 117-133

  Berzins, Martin ^a   Capon, Philip J ^b   Jimack, Peter K ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b Tessella Support Services plc ^*  (United Kingdom)

Author keywords

Adaptive remeshing; Interpolation errors; Method of lines

Indexed keywords

ERROR ANALYSIS; INTEGRATION; INTERPOLATION; NUMERICAL METHODS;

ADAPTIVE REMESHING; DISCRETE TIME STATIC REMESHING; METHOD OF LINES;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0031633524     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(97)00091-3     Document Type: Article

References (25)

1. I. Babuška, J. Chandra and J.E. Flaherty, Adaptive computational methods for PDEs, in: Proceedings of Workshop at University of Maryland (SIAM Publications, Philadelphia, PA, 1983).
2. R.E. Bank, PLTMG: a Software Package for Solving Elliptic Partial Differential Equations, Users Guide 7.0, Frontiers in Applied Mathematics 15 (SIAM Publications, Philadelphia, PA, 1994).
3. R.E. Bank, Private communication (1997).
4. 1 interpolant for codes based on backward differentiation formulae, Appl. Numer. Math. 2 (1986) 109-118.
5. M. Berzins, P.M. Dew and R.M. Furzeland, Developing software for time-dependent problems using the method of lines and differential-algebraic integrators, Appl. Numer. Math. 5 (1989) 373-397.
6. M. Berzins and R.M. Furzeland, A user's manual for SPRINT - a versatile software package for solving systems of algebraic ordinary and partial differential equations. Part 2: Partial differential equations, Report TNER.86.050, Shell Research Ltd, Thornton Research Centre, Chester, UK (1986).
7. M.O. Bristeau, R. Glowinski, L. Dutto, J. Périaux and G. Roge, Compressible viscous flow calculations using compatible finite element approximations, Internat. J. Numer. Methods Fluids 11 (1990) 719-749.
8. P.J. Capon, Adaptive stable finite element methods for the compressible Navier-Stokes equations, Ph.D. Thesis, University of Leeds (1995).
9. R.E. Ewing, Adaptive mesh refinements in large scale fluid-flow simulation, in: I. Babuška, O.C. Zienkiewicz, J. Gago and E.R. de A. Oliviera, eds., Accuracy Estimates and Adaptive Refinements in Finite Element Computations (Wiley, New York 1986) Chapter 16.
10. J.E. Flaherty, P.J. Paslow, M.S. Shephard and J.D. Vasilakis, Adaptive Methods for Partial Differential Equations (SIAM Publications, Philadelphia, PA, 1989).
11. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics 14 (Springer, Berlin, 1991).
12. G. Hauke and T.J.R. Hughes, A unified approach to compressible and incompressible flows, Comput. Methods Appl. Mech. Engrg. 113 (1994) 389-395.
13. J.M. Hyman and M.J. Naughton, Static rezone methods for tensor product grids, in: Lectures in Applied Mathematics 22 (American Mathematical Society, Providence, RI, 1985) 321-343.
14. P.K. Jimack, A new approach to finite element error control for time-dependent problems, in: M.J. Baines and K.W. Morton, eds., Numerical Methods for Fluid Dynamics 4 (Oxford University Press, Oxford, 1993) 567-573.
15. P.K. Jimack and A.J. Wathen, Temporal derivatives in the finite element method on continuously deforming grids, SIAM J. Numer. Anal. 28 (1991) 990-1003.
16. C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method (Cambridge University Press, Cambridge, 1987).
17. P. Lancaster and K. Šalkauskas, Curve and Surface Fitting (Academic Press, New York, 1986).
18. R. Lohner, An adaptive finite element scheme for transient problems in CFD, Comput. Methods Appl. Mech. Engrg. 50 (1987) 323-338.
19. B.J. Lucicr, A moving mesh numerical method for hyperbolic conservation laws, Math. Comp. 46 (1981) 59-69.
20. K. Miller and R. Miller, Moving finite elements: Part I, SIAM J. Numer. Anal. 18 (1981) 1019-1032.
21. F. Shakib, T.J.R. Hughes, and Z. Johan, A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. 89 (1991) 141-219.
22. L.F. Shampine, Numerical Solution of Ordinary Differential Equations (Chapman and Hall. 1994).
23. R.D. Skeel, Construction of variable stepsize multistep formulas, Math. Comp. 47 (176) (1986) 503-510.
24. R.D. Skeel and M. Berzins, A method for the spatial discretization of parabolic equations in one space variable, SIAM J. Sci. Statist. Comput. 11 (1990) 1-32.
25. A. Soulaimani and M. Fortin, Finite element solution of compressible viscous flows using conservative variables, Comput. Methods Appl. Mech. Engrg. 118 (1994) 319-350.