Optimality of a standard adaptive finite element method

Foundations of Computational Mathematics

Volumn 7, Issue 2, 2007, Pages 245-269

  Stevenson, Rob ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

A posteriori error estimator; Adaptive finite element method; Nonlinear approximation; Optimal computational complexity

Indexed keywords

ADAPTIVE FINITE ELEMENT METHODS; CONTINUOUS PIECEWISE-LINEAR FUNCTION; NONLINEAR APPROXIMATION; NUMBER OF TRIANGLES; OPTIMAL COMPUTATIONAL COMPLEXITY; PIECE-WISE CONSTANTS; PIECEWISE LINEAR APPROXIMATIONS; POSTERIORI ERROR ESTIMATOR;

COMPUTATIONAL COMPLEXITY; FINITE ELEMENT METHOD; PIECEWISE LINEAR TECHNIQUES; RATE CONSTANTS;

OPTIMIZATION;

EID: 34250183086     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s10208-005-0183-0     Document Type: Article

References (17)

1. M. Ainsworth and J. T. Oden, A Posteriori Error Estimation in Finite Element Analysis, Pure and Applied Mathematics, Wiley-Interscience, New York, 2000.
2. I. Babuška and M. Vogelius, Feedback and adaptive finite element solution of one-dimensional boundary value problems, Numer. Math. 44(1) (1984).
3. E. Bänsch, Local mesh refinement in 2 and 3 dimensions, Impact Comput. Sci. Engrg. 3(3) (1991), 181-191.
4. P. Binev, W. Dahmen, and R. DeVore, Adaptive finite element methods with convergence rates, Numer. Math. 97(2) (2004), 219-268.
5. P. Binev, W. Dahmen, R. DeVore, and P. Petruchev, Approximation classes for adaptive methods, Serdica Math. J. 28 (2002), 391-416.
6. P. Clément, Approximation by finite element functions using local regularization, RAIRO Anal. Numér. 9 (1975), 77-84.
7. S. Dahlke, Besov regularity for elliptic boundary value problems in polygonal domains, Appl. Math. Lett. 12(6) (1999), 31-36.
8. S. Dahlke and R. DeVore, Besov regularity for elliptic boundary value problems, Comm. Partial Differential Equations 22(1&2) (1997), 1-16.
9. W. Dörfler, A convergent adaptive algorithm for Poisson's equation, SIAM J. Numer. Anal. 33 (1996), 1106-1124.
10. W. F. Mitchell, A comparison of adaptive refinement techniques for elliptic problems, ACM Trans. Math. Software 15(4) (1989), 326-347.
11. P. Morin, R. Nochetto, and K. Siebert, Data oscillation and convergence of adaptive FEM, SIAM J. Numer. Anal. 38(2) (2000), 466-488.
12. P. Oswald, Multilevel Finite Element Approximation: Theory and applications, B.G. Teubner, Stuttgart, 1994.
13. L. R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp. 54(190) (1990), 483-493.
14. R. P. Stevenson, The completion of locally refined simplicial partitions created by bisection, Math. Comp. (2006) (to appear).
15. R. P. Stevenson, An optimal adaptive finite element method, SIAM J. Numer. Anal. 42(5) (2005), 2188-2217.
16. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley-Teubner, Chichester, UK, 1996.
17. H. Wu and Z. Chen, Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second-order elliptic problems, Research Report 2003-07, Institute of Computational Mathematics, Chinese Academy of Sciences, 2003.