A posteriori error estimates for nonlinear problems. $L^r$-estimates for finite element discretizations of elliptic equations

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1. [1] R. A. ADAMS, Sobolev Spaces. Academic Press, New York, 1975. Zbl0314.46030MR450957
2. [2] I. BABUŠKA and W. C. RHEINBOLDT, Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 15, 736-754 (1978). Zbl0398.65069MR483395
3. [3] I. BABUŠKA and W. C. RHEINBOLDT, A posteriori error estimates for the finite element method. Int. J. Numer. Methods in Engrg. 12, 1597-1615 (1978). Zbl0396.65068
4. [4] E. BÄNSCH and K. G. SIEBERT, A posteriori error estimation for nonlinear problems by dual techniques. Preprint, Universität Freiburg, 1995. 
5. [5] C. BERNARDI, B. MÉTIVET and R. VERFÜRTH, Analyse numérique d'indicateurs d'erreur. Preprint R 93025, Université Paris VI, 1993. 
6. [6] P. G. CIARLET, The Finite Element Method for Elliptic Problems. North Holland, Amsterdam, 1978. Zbl0383.65058MR520174
7. [7] P. CLÉMENT, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9, 77-84 (1975). Zbl0368.65008MR400739
8. [8] M. DAUGE, Elliptic Boundary Value Problems on Corner Domains. Springer, Lecture Notes in Mathematics 1341, Berlin, 1988. Zbl0668.35001MR961439
9. [9] K. ERIKSSON, An adaptive finite element method with efficient maximum norm error control for elliptic problems. Math. Models and Math. in Appl. Sci. 4, 313-329 (1994). Zbl0806.65106MR1282238
10. [10] K. ERIKSSON and C. JOHNSON, An adaptive finite element method for linear elliptic problems. Math. Comput. 50, 361-383 (1988). Zbl0644.65080MR929542
11. [11] K. ERIKSSON and C. JOHNSON, Adaptive finite element methods for parabolic problems I. A linear model problem. SIAM J. Numer. Anal. 28, 43-77 (1991). Zbl0732.65093MR1083324
12. [12] K. ERIKSSON and C. JOHNSON, Adaptive finite element methods for parabolic problems IV. Nonlinear problems. Chalmers University of Göteborg, Preprint 1992, 44 (1992). Zbl0835.65116MR1360457
13. [13] V. GIRAULT and P. A. RAVIART, Finite Element Approximation of the Navier-Stokes Equations. Computational Methods in Physics, Springer, Berlin, 2nd édition, 1986. Zbl0413.65081MR548867
14. [14] P. GRISVARD, Elliptic Problems in Nonsmooth Domains. Pitman, Boston, 1985. Zbl0695.35060MR775683
15. [15] C. JOHNSON and P. HANSBO, Adaptive finite element methods in computational mechanics. Comp. Math. Appl. Mech. Engrg. 101, 143-181 (1992). Zbl0778.73071MR1195583
16. [16] R. H. NOCHETTO, Pointwise a posteriori error estimates for elliptic problems on highly graded meshes. Math. Comput. 64, 1-22 (1995). Zbl0920.65063MR1270622
17. [17] J. POUSIN and J. RAPPAZ, Consistency, stability, a priori, and a posteriori errors for Petrov-Galerkin methods applied to nonlinear problems. Numer. Math. 69, 213-231 (1994). Zbl0822.65034MR1310318
18. [18] R. VERFÜRTH, A posteriori error estimates for nonlinear problems. Finite element discretizations of elliptic equations. Math. Comput. (206), 445-475 (1994). Zbl0799.65112MR1213837
19. [19] R. VERFÜRTH, A posteriori error estimates for nonlinear problems. Finite element discretizations of parabolic problems. Bericht Nr. 180, Ruhr-Universität Bochum, 1995. Zbl0869.65067
20. [20] R. VERFÜRTH, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner Series in advances in numerical mathematics, Stuttgart, 1996. Zbl0853.65108