A posteriori finite element error control for the P-laplace problem

SIAM Journal on Scientific Computing

Volumn 25, Issue 3, 2003, Pages 792-814

  Carstensen, Carsten ^a   Klose, R ^b  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF KIEL   (Germany)

Author keywords

A posteriori error estimates; Adaptive finite element method; Averaging error estimator; P Laplacian

Indexed keywords

CALCULATIONS; EIGENVALUES AND EIGENFUNCTIONS; ERROR CORRECTION; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; NUMERICAL ANALYSIS;

ADAPTIVE FINITE ELEMENT METHOD; ERROR ESTIMATOR; P-LAPLACIAN;

LAPLACE TRANSFORMS;

EID: 0242598086     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502416617     Document Type: Article

References (24)

1. [AO] M. AINSWORTH AND J. T. ODEN, A Posteriori Error Estimation in Finite Element Analysis, John Wiley & Sons, New York, 2000.
2. [ACF] J. ALBERTY, C. CARSTENSEN, AND S. A. FUNKEN, Remarks around 50 lines of MATLAB: Short finite element implementation, Numer. Algorithms, 20 (1999), pp. 117-137.
3. [BL] J. W. BARRETT AND W. B. LIU, Finite Element Approximation of the p-Laplacian, Math. Comp., 61 (1993), pp. 523-537.
4. [BC] S. BARTELS AND C. CARSTENSEN, Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM, Math. Comp., 71 (2002), pp. 971-994 (electronic).
5. [BSc] S. C. BRENNER AND L. R. SCOTT, The Mathematical Theory of Finite Element Methods, Texts Appl. Math. 15, Springer, New York, 1994.
6. [Ca] C. CARSTENSEN, Quasi-interpolation and a posteriori error analysis in finite element methods, M2AN Math. Model. Numer. Anal., 33 (1999), pp. 1187-1202.
7. [CB] C. CARSTENSEN AND S. BARTELS, Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids Part I: Low order conforming, nonconforming, and mixed FEM, Math. Comp., 71 (2002), pp. 945-969.
8. [CF1] C. CARSTENSEN AND S. A. FUNKEN, Constants in Clément- interpolation error and residual based a posteriori error estimates in finite element methods, East-West Numer. Anal., 8 (2000), pp. 153-175.
9. [CF2] C. CARSTENSEN AND S. A. FUNKEN, Averaging technique for fe - a posteriori error control in elasticity. Part I: Conforming FEM, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 2483-2498.
10. [CF3] C. CARSTENSEN AND S. A. FUNKEN, Averaging technique for fe - a posteriori error control in elasticity. Part II: λ-independent estimates, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 4663-4675.
11. [CF4] C. CARSTENSEN AND S. A. FUNKEN, Averaging technique for fe - a posteriori error control in elasticity. Part III: Locking-free nonconforming FEM, Comput. Methods Appl. Mech. Engrg., 191 (2001), pp. 861-877.
12. [CF5] C. CARSTENSEN AND S. A. FUNKEN, A posteriori error control in low-order finite element discretisations of incompressible stationary flow problems, Math. Comp., 70 (2001), pp. 1353-1381.
13. [CF6] C. CARSTENSEN AND S. A. FUNKEN, Fully reliable localized error control in the FEM, SIAM J. Sci. Comput., 21 (2000), pp. 1465-1484.
14. [CP] C. CARSTENSEN AND P. PLECHAC, Numerical solution of the scalar double-well problem allowing microstructure, Math Comp., 66 (1997), pp. 997-1026.
15. [CV] C. CARSTENSEN AND R. VERFÜRTH, Edge residuals dominate a posteriori error estimates for low order finite element methods, SIAM J. Numer. Anal., 36 (1999), pp. 1571-1587.
16. [Ch] S.-S. CHOW, Finite element error estimates for non-linear elliptic equations of monotone type, Numer. Math., 54 (1989), pp. 373-393.
17. [Ci] P. G. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
18. [C1] P. CLÉMENT, Approximation by finite element functions using local regularization, RAIRO Sér. Rouge Anal. Numér., 9 (1975), pp. 77-84.
19. [MNS] P. MORIN, R. H. NOCHETTO, AND K. G. SIEBERT, Local Problems on Stars: A Posteriori Error Estimators, Convergence and Performance, preprint.
20. [LY1] W. LIU AND N. YAN, Quasi-norm local error estimators for p-Laplacian, SIAM J. Numer. Anal., 39 (2001), pp. 100-127.
21. [LY2] W. LIU AND N. YAN, Quasi-norm a priori and a posteriori error estimates for the nonconforming approximation of p-Laplacian, Numer. Math., 89 (2001), pp. 341-378.
22. [LY3] W. LIU AND N. YAN, On quasi-norm interpolation error estimation and a posteriori error estimates for p-Laplacian, SIAM J. Numer. Anal., 40 (2002), pp. 1870-1895.
23. [V] R. VERPÜRTH, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley-Teubner, Stuttgart, 1996.
24. [ZZ] O. C. ZIENKIEWICZ AND J. Z. ZHU, A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. Numer. Methods Engrg., 24 (1987), pp. 337-357.