Optimal convergence for the finite element method in Campanato spaces

Mathematics of Computation

Volumn 68, Issue 228, 1999, Pages 1397-1427

  Dolzmann, Georg ^a  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

Campanato spaces; Finite element methods; Optimal error estimates

Indexed keywords

EID: 0033425858     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-99-01175-8     Document Type: Article

References (48)

1. N. E. Aguilera, L. A. Caffarelli, Regularity results for discrete solutions of second order elliptic problems in the finite element method, Calcolo 23 (1986), 327-353. MR 89h:65171
2. N. E. Aguilera, L. A. Caffarelli, Regularity results for discrete solutions of second order elliptic problems in the finite element method, Calcolo 23 (1986), 327-353. MR 89h:65171
3. H. Blum, Q. Lin, R. Rannacher, Asymptotic error expansion and Richardson extrapolation for linear finite elements, Numer. Math. 49 (1986), 11-37. MR 87m:65172
4. H. Blum, Q. Lin, R. Rannacher, Asymptotic error expansion and Richardson extrapolation for linear finite elements, Numer. Math. 49 (1986), 11-37. MR 87m:65172
5. S. C. Brenner, L. R. Scott, The Mathematical Theory of Finite Element Methods, Springer, New York, 1994 MR 95f:65001
6. S. C. Brenner, L. R. Scott, The Mathematical Theory of Finite Element Methods, Springer, New York, 1994 MR 95f:65001
7. 2,λ Ann. Mat. Pura Appl. 69 (1965), 321-381. MR 33:395
8. 2,λ Ann. Mat. Pura Appl. 69 (1965), 321-381. MR 33:395
9. S. Campanato, Sistemi ellittici in forma divergenza. Regolarità all'interno, Quaderni, Scuola Normale Superiore, Pisa, 1980. MR 83i:35067
10. S. Campanato, Sistemi ellittici in forma divergenza. Regolarità all'interno, Quaderni, Scuola Normale Superiore, Pisa, 1980. MR 83i:35067
11. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. MR 58:25001
12. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. MR 58:25001
13. G. Dolzmann, Campanato-Ungleichungen für Differenzenverfahren und finite Elemente, Bonner Mathematische Schriften 251 (1994). MR 95h:65081
14. G. Dolzmann, Campanato-Ungleichungen für Differenzenverfahren und finite Elemente, Bonner Mathematische Schriften 251 (1994). MR 95h:65081
15. G. Dolzmann, J. Frehse, Optimale asymptotische Konvergenz linearer finite Elemente bei elliptischen Problemen mit Campanato-Abschätzungen, Bonner Mathematische Schriften 228 (1991), 95-120. MR 93j:65177
16. G. Dolzmann, J. Frehse, Optimale asymptotische Konvergenz linearer finite Elemente bei elliptischen Problemen mit Campanato-Abschätzungen, Bonner Mathematische Schriften 228 (1991), 95-120. MR 93j:65177
17. p theory, manuscr. math. 88 (1995), 261-273. MR 96g:35054
18. p theory, manuscr. math. 88 (1995), 261-273. MR 96g:35054
19. R. G. Durán, Quasi-optimal estimates for finite element approximations using Orlicz norms, Math. Comp. 49 (1987), 17-23. MR 88d:65160
20. R. G. Durán, Quasi-optimal estimates for finite element approximations using Orlicz norms, Math. Comp. 49 (1987), 17-23. MR 88d:65160
21. R. G. Durán, A note on the convergence of linear finite elements, SIAM J. Numer. Anal. 25 (1988), 1032-1036. MR 89g:65141
22. R. G. Durán, A note on the convergence of linear finite elements, SIAM J. Numer. Anal. 25 (1988), 1032-1036. MR 89g:65141
23. M. Fuchs, The Green matrix for strongly elliptic systems of second order with continuous coefficients, Z. Anal. Anwendungen. 5 (1986), 507-531. MR 89a:35069
24. M. Fuchs, The Green matrix for strongly elliptic systems of second order with continuous coefficients, Z. Anal. Anwendungen. 5 (1986), 507-531. MR 89a:35069
25. M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton University Press, 1983. MR 86b:49003
26. M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton University Press, 1983. MR 86b:49003
27. E. Giusti, Metodi diretti nel calcolo delle variazioni, Unione Matematica Italiana, Bologna, 1994.
28. F. John, L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. MR 23:A1348
29. F. John, L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. MR 23:A1348
30. A. Kufner, O. John, S. Fučik, Function Spaces, Noordhoff, Leyden, 1977. MR 58:2189
31. A. Kufner, O. John, S. Fučik, Function Spaces, Noordhoff, Leyden, 1977. MR 58:2189
32. F. Natterer, Über die punktweise Konvergenz finiter Elemente, Num. Math. 25 (1975), 67-77. MR 57:14514
33. F. Natterer, Über die punktweise Konvergenz finiter Elemente, Num. Math. 25 (1975), 67-77. MR 57:14514
34. J. A. Nitsche, Schauder Estimates for Finite Element Approximations on Second Order Elliptic Boundary Value Problems, Proceedings of a Special Year in Numerical Analysis, University of Maryland, Numerical Analysis Lecture Notes 20, 1981.
35. R. Rannacher, Zur L∞-Konvergenz linearer finiter Elemente beim Dirichlet-Problem, Math. Z. 149 (1976), 69-77. MR 58:8361
36. R. Rannacher, Zur L∞-Konvergenz linearer finiter Elemente beim Dirichlet-Problem, Math. Z. 149 (1976), 69-77. MR 58:8361
37. R. Rannacher, R. Scott, Some optimal error estimates for piecewise linear finite element approximations, Math. Comp. 38 (1982), 437-445. MR 83e:65180
38. R. Rannacher, R. Scott, Some optimal error estimates for piecewise linear finite element approximations, Math. Comp. 38 (1982), 437-445. MR 83e:65180
39. 1,2-projection into finite element spaces, Math. Comp. 38 (1982), 1-22. MR 82m:65106
40. 1,2-projection into finite element spaces, Math. Comp. 38 (1982), 1-22. MR 82m:65106
41. A. H. Schatz, L.B. Wahlbin, Interior maximum-norm estimates for finite element methods, Part II Math. Comp. 64 (1995), 907-928. MR 95j:65143
42. A. H. Schatz, L.B. Wahlbin, Interior maximum-norm estimates for finite element methods, Part II Math. Comp. 64 (1995), 907-928. MR 95j:65143
43. L. R. Scott, S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp. 54 (1990), 483-493. MR 90j:65021
44. L. R. Scott, S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp. 54 (1990), 483-493. MR 90j:65021
45. p,λ and interpolation, Ann. Scuola Norm. Sup. Pisa (3) 25 (1965), 443-462. MR 33:7480
46. p,λ and interpolation, Ann. Scuola Norm. Sup. Pisa (3) 25 (1965), 443-462. MR 33:7480
47. K. Zhang, A counterexample in the theory of coerciveness for elliptic systems, J. Partial Differential Equations 2 (1989), 79-82. MR 81d:35067
48. K. Zhang, A counterexample in the theory of coerciveness for elliptic systems, J. Partial Differential Equations 2 (1989), 79-82. MR 81d:35067