Stable finite elements for problems with wild coefficients

SIAM Journal on Numerical Analysis

Volumn 33, Issue 3, 1996, Pages 890-916

  Vavasis, Stephen A ^a  

^a School of Operations Research and Information Engineering   (United States)

Author keywords

Equilibrium systems; Finite elements; Numerical stability; Variable coefficients

Indexed keywords

EID: 1542745115     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/0733045     Document Type: Article

References (30)

1. A. V. AHO, J. E. HOPCROFT, AND J. D. ULLMAN, Data Structures and Algorithms, Addison-Wesley, Reading, MA, 1983.
2. I. BABUŠKA, G. CALOZ, AND J. E. OSBORN, Special finite element methods for a class of second order elliptic problems with rough coefficients, SIAM J. Numer. Anal., 31 (1994), pp. 945-981.
3. I. BABUŠKA AND J. E. OSBORN, Generalized finite element methods: Their performance and their relation to mixed methods, SIAM J. Numer. Anal., 20 (1983), pp. 510-536.
4. B. S. BAKER, E. GROSSE, AND C. S. RAFFERTY, Nonobtuse triangulation of polygons, Discrete Comput. Geom., 3 (1988), pp. 147-168.
5. M. BERN AND D. EPPSTEIN, Mesh generation and optimal triangulation, in Computing in Euclidean Geometry, D. Z. Du and F. Hwang, eds., World Scientific, River Edge, NJ, 1992.
6. M. BERN, D. EPPSTEIN, AND J. GILBERT, Provably good mesh generation, J. Comput. System Sci., 48 (1994), pp. 384-409.
7. A. BJÖRCK, Least squares methods, in Handbook of Numerical Analysis, Vol. I, P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam, 1990.
8. J. H. BRAMBLE, J. E. PASCIAK, AND A. H. SCHATZ, An iterative method for elliptic problems on regions partitioned into substructures, Math. Comp., 46 (1986), pp. 361-369.
9. F. BREZZI AND M. FORTIN, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
10. P. G. CIARLET, Basic error estimates for elliptic problems, in Handbook of Numerical Analysis, Vol. II, P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam, 1991.
11. P. CONCUS AND G. GOLUB, Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations, SIAM J. Numer. Anal., 10 (1973), pp. 1103-1120.
12. M. DOBROWOLSKI, Numerical Approximation of Elliptic Interface and Corner Problems, Habilitationsschrift, University of Bonn, 1981.
13. R. S. FALK AND J. E. OSBORN, Remarks on Mixed Finite Element Methods for Problems with Rough Coefficients, Math. Comp., 62 (1994), pp. 1-19.
14. A. GEORGE AND J. W. H. LIU, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981.
15. R. B. KELLOGG, Singularities in interface problems, in Numerical Solution of Partial Differential Equations II, B. Hubbard, ed., Academic Press, New York, 1971.
16. E. MELISSARATOS AND D. SOUVAINE, Coping with inconsistencies: A new approach to produce quality triangulations of polygonal domains with holes, in Proc. 8th Symp. on Computational Geometry, ACM Press, 1992, pp. 202-211.
17. S. A. MITCHELL AND S. A. VAVASIS, Quality mesh generation in three dimensions, in Proc. 8th Symp. on Computational Geometry, ACM Press, 1992, pp. 212-221.
18. D. P. O'LEARY, On bounds for scaled projections and pseudoinverses, Linear Algebra Appl., 132 (1990), pp. 115-117.
19. J. ORTEGA, Numerical Analysis: A Second Course, Academic Press, New York, San Diego, 1972.
20. M. H. PROTTER AND H. F. WEINBERGER, Maximum Principles in Differential Equations, Springer-Verlag, New York, 1984.
21. J. E. ROBERTS AND J. M. THOMAS, Mixed and hybrid methods, in Handbook of Numerical Analysis, Vol. II, P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam, 1991.
22. A. H. SCHATZ, Unpublished lectures, University of Bonn, 1980.
23. G. W. STEWART, On scaled projections and pseudoinverses, Linear Algebra Appl., 112 (1989), pp. 189-193.
24. G. STRANG, Introduction to Applied Mathematics, Wellesley-Cambridge Press, Wellesley, MA, 1986.
25. _, A framework for equilibrium equations, SIAM Rev., 30 (1988), pp. 283-297.
26. G. STRANG AND G. J. FIX, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ, 1973.
27. M. J. TODD, A Dantzig-Wolfe-like variant of Karmarkar's interior-point linear programming algorithm, Oper. Res., 38 (1990), pp. 1006-1018.
28. S. A. VAVASIS, Stable numerical algorithms for equilibrium systems, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 1108-1131.
29. L. WAHLBIN, Private communication, 1993.
30. A. J. WATHEN, B. FISCHER, AND D. J. SILVESTER, The convergence rate of the minimum residual method for the Stokes problem, Numer. Math., 71 (1995), pp. 121-134.