Interpolation of non-smooth functions on anisotropic finite element meshes
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 6, pp. 1149-1185.
@article{M2AN_1999__33_6_1149_0,
     author = {Apel, Thomas},
     title = {Interpolation of non-smooth functions on anisotropic finite element meshes},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {1149--1185},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {6},
     year = {1999},
     mrnumber = {1736894},
     zbl = {0984.65113},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1999__33_6_1149_0/}
}
TY  - JOUR
AU  - Apel, Thomas
TI  - Interpolation of non-smooth functions on anisotropic finite element meshes
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1999
SP  - 1149
EP  - 1185
VL  - 33
IS  - 6
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/M2AN_1999__33_6_1149_0/
LA  - en
ID  - M2AN_1999__33_6_1149_0
ER  - 
%0 Journal Article
%A Apel, Thomas
%T Interpolation of non-smooth functions on anisotropic finite element meshes
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1999
%P 1149-1185
%V 33
%N 6
%I EDP-Sciences
%U http://www.numdam.org/item/M2AN_1999__33_6_1149_0/
%G en
%F M2AN_1999__33_6_1149_0
Apel, Thomas. Interpolation of non-smooth functions on anisotropic finite element meshes. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 6, pp. 1149-1185. http://www.numdam.org/item/M2AN_1999__33_6_1149_0/

[1] Th. Apel, Finite-Elemente-Methoden über lokal verfeinerten Netzen für elliptische Probleme in Gebieten mit Kanten. Ph.D. thesis, TU Chemnitz (1991). | Zbl

[2] Th. Apel, Anisotropic interpolation error estimates for isoparametric quadrilateral finite elements. Computing 60 (1998)157-174. | MR | Zbl

[3] Th. Apel, Anisotropic finite elements: Local estimates and applications. Teubner, Stuttgart (1999). | MR | Zbl

[4] Th. Apel and M. Dobrowolski, Anisotropic interpolation with applications to the finite element method. Computing 47 (1992) 277-293. | MR | Zbl

[5] Th. Apel and B. Heinrich, Mesh refinement and windowing near edges for some elliptic problem. SIAM J. Numer. Anal. 31 (1994) 695-708. | MR | Zbl

[6] Th. Apel and G. Lube, Anisotropic mesh refinement in stabilized Galerkin methods. Numer. Math. 74 (1996) 261-282. | MR | Zbl

[7] Th. Apel and G. Lube, Anisotropic mesh refinement for a singularly perturbed reaction diffusion model problem. Appl. Numer. Math. 26 (1998) 415-433. | MR | Zbl

[8] Th. Apel and F. Milde, Comparison of several mesh refinement strategies near edges. Comm. Numer. Methods Engrg, 12 (1996) 373-381. | Zbl

[9] Th. Apel and S. Nicaise, Elliptic problems in domains with edges: anisotropic regularity and anisotropic finite element meshes, in Partial Differential Equations and Functional Analysis (In Memory of Pierre Grisvard), J. Cea, D. Chenais, G. Geymonat, and J.L. Lions Eds., Birkhäuser, Boston (1996) 18-34. Shortened version of Preprint SPC94_16, TU Chemnitz-Zwickau (1994). | MR | Zbl

[10] Th. Apel and S. Nicaise, The finite element method with anisotropic mesh grading for the Poisson problem in domains with edges. Technical report, TU Chemnitz-Zwickau (1996). Improved version of Preprint SPC94_16, TU Chemnitz-Zwickau (1994), available only via ftp, server ftp.tu-chemnitz.de, directory pub/Local/mathematik/Apel, file anl.ps.Z.

[11] Th. Apel and S. Nicaise, The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges. Math. Methods Appl. Sci. 21 (1998) 519-549. | MR | Zbl

[12] Th. Apel, A.-M. Sändig and J. R. Whiteman, Graded mesh refinement and error estimates for finite element solutions of elliptic boundary value problems in non-smooth domains. Math. Methods Appl. Sci. 19 (1996) 63-85. | MR | Zbl

[13] I. Babuška, R. B. Kellogg and J. Pitkäranta, Direct and inverse error estimates for finite elements with mesh refinements.Numer. Math. 33 (1979) 447-471. | MR | Zbl

[14] A. E. Beagles and J. R. Whiteman, Finite element treatment of boundary singularities by augmentation with non-exact singular functions. Numer. Methods Partial Differential Equations 2 (1986) 113-121. | MR | Zbl

[15] R. Becker, An adaptive finite element method for the incompressible Navier-Stokes equations on time-dependent domains. Ph.D. thesis, Ruprecht-Karls-Universität Heidelberg (1995). | Zbl

[16] J. H. Bramble and S. R. Hilbert, Estimation of linear functionals on Sobolev spaces with applications to Fourier transforms and spline interpolation. SIAM J. Numer. Anal 7 (1970) 112-124. | MR | Zbl

[17] J. H. Bramble and S. R. Hilbert, Bounds for a class of linear functionals with applications to Hermite interpolation. Numer. Math. 16 (1971) 362-369. | MR | Zbl

[18] P. G. Ciarlet, The finite element method for elliptic problems. North-Holland, Amsterdam (1978). | MR | Zbl

[19] P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77-84. | Numdam | MR | Zbl

[20] M. Dobrowolski and H.-G Roos, A priori estimates for the solution of convection-diffusion problems and interpolation on Shishkin meshes. Z. Anal. Anwendungen 16 (1997) 1001-1012. | MR | Zbl

[21] T. Dupont and R. Scott, Polynomial approximation of functions in Sobolev spaces. Math. Comput. 34 (1980) 441-463. | MR | Zbl

[22] R. G. Durán, Error estimates for 3-d narrow finite elements. Math. Comput. 68 (1999) 187-199. | MR | Zbl

[23] A. Kufner and A.-M. Sandig, Some Applications of Weighted Sobolev Spaces. Teubner, Leipzig (1987). | MR | Zbl

[24] G. Kunert, Error estimation for anisotropic tetrahedral and triangular finite element meshes. Preprint SFB393/97-17, TUChemnitz (1997).

[25] M. S. Lubuma and S. Nicaise, Dirichlet problems in polyhedral domains II: approximation by FEM and BEM. J. Comput. Appl. Math. 61 (1995) 13-27. | MR | Zbl

[26] M. S. Lubuma and S. Nicaise, Finite element method for elliptic problems with edge corners. J.Comput. Appl. Math, (submitted). | Zbl

[27] L. A. Oganesyan and L. A. Rukhovets, Variational-difference methods for the solution of elliptic equations. Izd. Akad. Nauk Armyanskoi SSR, Jerevan (1979). In Russian. | MR | Zbl

[28] P. Oswald, Multilevel Finite Element Approximation: Theory and Applications. Teubner, Stuttgart (1994). | MR | Zbl

[29] T. Von Petersdorff, Randwertprobleme der Elastizitätstheorie für Polyeder - Singularitäten und Approximationen mit Randelementmethoden. Ph.D. thesis, TH Darmstadt (1989). | Zbl

[30] L. R. Scott and S. Zhang, Finite element interpolation of non-smooth functions satisfying boundary conditions. Math. Comp.54 (1990) 483-493. | MR | Zbl

[31] N. A. Shenk, Uniform error estimates for certain narrow Lagrangian finite elements. Math. Comp. 63 (1994) 105-119. | MR | Zbl

[32] K. Siebert, An a posteriori error estimator for anisotropic refinement. Numer. Math. 73 (1996) 373-398. | MR | Zbl

[33] E. P. Stephan and J. R. Whiteman, Singularities of the Laplacian at corners and edges of three-dimensional domains and their treatment with finite element methods. Math. Methods Appl Sci. 10 (1988) 339-350. | MR | Zbl

[34] H. Walden and R. B. Kellogg, Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical domain. J. Engrg. Math. 11 (1977) 299-318. | MR | Zbl