A new moving mesh algorithm for the finite element solution of variational problems

SIAM Journal on Numerical Analysis

Volumn 35, Issue 4, 1998, Pages 1416-1438

  Tourigny, Yves ^a   Hülsemann, Frank ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Finite elements; Grid generation; Moving mesh; Triangulation; Variational problems

Indexed keywords

EID: 0000816388     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142996313932     Document Type: Article

References (20)

1. 2 fits to continuous functions with adjustable nodes in one and two dimensions, Math. Comp., 62 (1994), pp. 645-669.
2. M.J. BAINES, Moving Finite Elements, Clarendon Press, Oxford, UK, 1994.
3. M.J. BAINES, Use of a Discrete Norm in Best Piecewise Constant Approximation of Continuous Functions on Irregular Grids, Numerical Analysis report 6/95, University of Reading, UK, 1995.
4. R.E. BANK, PLTMG Users Guide 7.0, SIAM, Philadelphia, 1994.
5. D.L. BARROW, C.K. CHUI, P.W. SMITH, AND J.D. WARD, Unicity of best mean approximation by second order splines with variable knots, Math. Comp., 32 (1978), pp. 1131-1143.
6. A. BRANDT, Multi-level adaptive solutions to boundary-value problems, Math. Comp., 31 (1977), pp. 333-390.
7. G.R. COWPER, Gaussian quadrature formulas for triangles, Internat. J. Numer. Methods Engrg., 7 (1973), pp. 405-410.
8. M. DELFOUR, G. PAYRE, AND J.P. ZOLÉSIO, An optimal triangulation for second-order elliptic problems, Comput. Methods Appl. Mech. Engrg., 50 (1985), pp. 231-261.
9. P. DE OLIVEIRA, Existence de maillages optimaux dans les méthodes d' éléments finis, RAIRO Anal. Numér., 14 (1980), pp. 279-290.
10. I. EKELAND AND R. TEMAM, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976.
11. C.A. FELIPPA, Optimization of finite element grids by direct energy search, Appl. Math. Modelling, 1 (1976), pp. 93-96.
12. C.A. FELIPPA, Numerical experiments in finite element grid optimization by direct energy search, Appl. Math. Modelling, 1 (1977), pp. 239-244.
13. M. FORTIN AND R. GLOWINSKI, Méthodes de Lagrangien Augmenté, Dunod, Paris, 1982.
14. 1 -approximation via an algorithm, Math. Comp., 65 (1996), pp. 647-660.
15. W. HUANG, Y. REN, AND R.D. RUSSELL, Moving mesh PDEs based on the equidistribution principle, SIAM J. Numer. Anal., 31 (1994), pp. 709-730.
16. C. JOHNSON, Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge University Press, Cambridge, UK, 1987.
17. 1 interpolation, in Mathematical Software III, J.R. Rice, ed., Academic Press, New York, 1977, pp. 161-194.
18. T.A. MANTEUFFEL AND S. MCCORMICK, Multilevel Projection Methods for First-Order Systems Least Squares, manuscript available at the ftp site amath.Colorado.edu\pub\multigrid\asme.ps
19. S. RIPPA AND B. SCHIFF, Minimum energy triangulations for elliptic problems, Comput. Methods Appl. Mech. Engrg., 84 (1990), pp. 257-274.
20. 2 approximation by discontinuous piecewise polynomials, Math. Comp., 66 (1997), pp. 623-650.