Geodesic
Functional a posteriori error estimates for the
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 127-146 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper, a general form of functional type a posteriori error estimates for linear reaction-convection-diffusion problems is presented. It is derived by purely functional arguments without attracting specific properties of the approximation method. The estimate provides a guaranteed upper bound of the difference between the exact solution and any conforming approximation from the energy functional class. It is also proved that the derived error majorants give computable quantities which are equivalent to the error evaluated in the energy and combined primal-dual norms. 
@article{ZNSL_2007_348_a4,
     author = {S. Nicaise and S. I. Repin},
     title = {Functional a posteriori error estimates for the},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {127--146},
     year = {2007},
     volume = {348},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a4/}
}
TY  - JOUR
AU  - S. Nicaise
AU  - S. I. Repin
TI  - Functional a posteriori error estimates for the
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2007
SP  - 127
EP  - 146
VL  - 348
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a4/
LA  - en
ID  - ZNSL_2007_348_a4
ER  - 
%0 Journal Article
%A S. Nicaise
%A S. I. Repin
%T Functional a posteriori error estimates for the
%J Zapiski Nauchnykh Seminarov POMI
%D 2007
%P 127-146
%V 348
%U http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a4/
%G en
%F ZNSL_2007_348_a4
S. Nicaise; S. I. Repin. Functional a posteriori error estimates for the. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 127-146. http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a4/

[1] A. Ern, J. Proft, “A posteriori Discontinuous Galerkin error estimates for transient convection-diffusion equations”, Appl. Math. Lett., 18 (2005), 833–841 | DOI | MR | Zbl

[2] D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin, 1977 | MR | Zbl

[3] C. Johnson, “Adaptive finite element methods for diffusion and convection problems”, Comput. Methods Appl. Mech. Engrg., 82 (1990), 301–322 | DOI | MR | Zbl

[4] O. A. Ladyzhenskaya, N. N. Uraltseva, Linear and Quasilinear Elliptic equations, Academic Press, New York, 1968 | MR | Zbl

[5] J. Medina, M. Picasso, J. Rappaz, Error estimates and adaptive finite elements for nonlinear diffusion-convection problems, Ecole Polytechnique Federale de Lausanne, Preprint CH-1015, 1995 | MR

[6] K. W. Morton, Numerical Solution of Convection-Diffusion Problems, Applied Mathematics and Mathematical Computation, 12, Chapman Hall, London, 1996 | MR | Zbl

[7] P. Neittaanmäki and S. Repin, Reliable methods for computer simulation, Error control and a posteriori estimates, Elsevier, New York, 2004 | MR | Zbl

[8] S. Nicaise, “A posteriori error estimation of some cell centered finite volume methods for diffusion-convection-reaction problems”, J. Numer. Anal., 44:3 (2006), 949–978 | DOI | MR | Zbl

[9] S. I. Repin, “Two-sided estimates of deviation from exact solutions of uniformly elliptic equations”, Proc. St.Petersburg Math. Soc., V. IX, Amer. Math. Soc. Transl. Ser. 2, 209, Amer. Math. Soc., Providence, RI, 2003, 143–171 | MR

[10] S. Repin, “A posteriori error estimation for variational problems with uniformly convex functionals”, Math. Comput., 69(230) (2000), 481–500 | MR | Zbl

[11] S. Repin, “Estimates of deviations from exact solutions for some boundary-value problems with incompressibility condition”, St.Petersburg Math. J., 16:5 (2004), 124–161 | MR

[12] S. Repin, S. Sauter, “Functional a posteriori estimates for the reaction-diffusion problem”, C. R. Acad. Sci. Paris, Ser. 1, 343 (2006), 349–354 | MR | Zbl

[13] R. Verfürth, “A posteriori error estimators for convection-diffusion problems”, Numer. Math., 80 (1998), 641–663 | DOI | MR | Zbl

[14] R. Verfürth, “Robust a posteriori error estimates for sationary convection-diffusion equations”, SIAM J. Numer. Anal., 43:4 (2005), 1766–1782 | DOI | MR | Zbl