New adaptive modification strategy for numerical solutions to elliptic boundary value problems

Applied Numerical Mathematics

Volumn 32, Issue 3, 2000, Pages 305-329

  Valenciano, José ^a   Owens, Robert G ^a,b  

^a EDINBURGH NAPIER UNIVERSITY   (United Kingdom)

^b EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE ALGORITHMS; APPROXIMATION THEORY; ERROR ANALYSIS; FINITE ELEMENT METHOD; INTERPOLATION; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; NUMERICAL METHODS; POLYNOMIALS; PROBLEM SOLVING; RESPONSE TIME (COMPUTER SYSTEMS); TENSORS;

CENTRAL PROCESSING UNIT; HELMHOLTZ EQUATIONS; MESH MODIFICATION STRATEGIES; SPECTRAL ELEMENT METHODS;

BOUNDARY VALUE PROBLEMS;

EID: 0034159349     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(99)00030-6     Document Type: Article

References (30)

1. [1] M. Ainsworth, B. Senior, An adaptive refinement strategy for hp-finite element computations, Appl. Numer. Math. 26 (1998) 165-178.
2. [2] I. Babuška, M. Suri, The h-p version of the finite element method with quasiuniform meshes, RAIRO Math. Modelling Numer. Anal. 21 (1987) 199-238.
3. [3] I. Babuška, M. Suri, The p-and h-p versions of the finite element method, an overview, Comput. Methods Appl. Mech. Engrg. 80 (1990) 5-26.
4. [4] C. Bernardi, Indicateurs d'erreur en h-N version des éléments spectraux, RAIRO Math. Modelling Numer. Anal. 30 (1996) 1-38.
5. [5] C. Bernardi, Y. Maday, A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in: H. Brezis and J.L. Lions, Eds., Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, Pitman Research Notes in Mathematics Series, Vol. 11, Longman, London/New York, 1994, pp. 13-51.
6. [6] C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods in Fluid Dynamics, Springer, Berlin, 1988.
7. [7] G.F. Carey, J.T. Oden, Finite Elements, Vol. II, A Second Course, Prentice-Hall, Englewood Cliffs, NJ, 1983.
8. [8] P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
9. [9] C. Cuvelier, A. Segal, A.A. van Steenhoven, Finite Element Methods and Navier-Stokes Equations, D. Reidel, Dordrecht, 1986.
10. [10] P.J. Davis, P. Rabinowitz, Methods of Numerical Integration, Academic Press, London/New York, 1984.
11. [11] L. Demkowicz, J.T. Oden, W. Rachowicz, O. Hardy, Toward a universal h-p adaptive finite element strategy, Part 1. Constrained approximation and data structure, Comput. Methods Appl. Mech. Engrg. 77 (1989) 79-112.
12. [12] K. Eriksson, D. Estep, P. Hansbo, C. Johnson, Introduction to adaptive methods for differential equations, Acta Numerica (1995) 105-158.
13. [13] D. Gottlieb, S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, PA, 1977.
14. [14] F. Ihlenburg, I. Babuška, Finite element solution of the Helmholtz equation with high wave number, Part II. The h-p version of the FEM, SIAM J. Numer. Anal. 34 (1997) 315-358.
15. [15] Y. Maday, C. Mavriplis, A.T. Patera, Nonconforming mortar element methods: application to spectral discretizations, in: T.F. Chan, R. Glowinski, J. Periaux and O.B. Widlund, Eds., Domain Decomposition Methods, SIAM, Philadelphia, PA, 1989, pp. 392-418.
16. [16] C. Mavriplis, Adaptive mesh strategies for spectral element methods, Comput. Methods Appl. Mech. Engrg. 116 (1994) 77-86.
17. [17] J.T. Oden, G.F. Carey, Finite Elements, Vol. IV, Mathematical Aspects, Prentice-Hall, Englewood Cliffs, NJ, 1983.
18. [18] J.T. Oden, L. Demkowicz, Advances in adaptive improvements. A survey of adaptive finite element methods in computational mechanics, in: A.K. Noor and J.T. Oden, Eds., State of the Art Surveys in Computational Mechanics, ASME, 1989, pp. 441-467.
19. [19] J.T. Oden, L. Demkowicz, W. Rachowicz, T. A. Westermann, Toward a universal h-p adaptive finite element strategy, Part 2. A posteriori error estimation, Comput. Methods Appl. Mech. Engrg. 77 (1989) 113-180.
20. [20] J.T. Oden, A. Patra, Y. Feng, An h-p adaptive strategy, AMD Adaptive, Multilevel, and Hierarchical Computational Strategies 157 (1992) 23-46.
21. [21] J.T. Oden, W. Wu, M. Ainsworth, An a posteriori error estimate for finite element approximations of the Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. 111 (1994) 185-202.
22. [22] J.T. Oden, W. Wu, V. Legat, An h-p adaptive strategy for finite element approximations of the Navier-Stokes equations, Internat. J. Numer. Methods Fluids 20 (1995) 831-851.
23. [23] R.G. Owens, T.N. Phillips, Steady viscoelastic flow past a sphere using spectral elements, Internat. J. Numer. Methods Engrg. 39 (1996) 1517-1534.
24. [24] R. Stenberg, M. Suri, Mixed hp finite element methods for problems in elasticity and Stokes flow, Numer. Math. 72 (1996) 367-389.
25. [25] M. Suri, private communication.
26. [26] R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, Revised Edition, North-Holland, Amsterdam, 1984.
27. [27] J. Valenciano, Ph.D. Thesis, Napier University, in progress.
28. [28] J. Valenciano, R.G. Owens, An h-p adaptive spectral element method for Stokes flow, Appl. Numer. Math., to appear.
29. [29] V. Warichet, V. Legat, Adaptive hp-finite element viscoelastic flow calculations, Comput. Methods Appl. Mech. Engrg. 136 (1996) 93-110.
30. [30] W. Wu, h-p adaptive methods for incompressible viscous flow problems, Ph.D. Thesis, The University of Texas, Austin, TX.