@article{ZVMMF_2005_45_8_a7,
author = {Yu. V. Vassilevski and K. N. Lipnikov},
title = {Error bounds for controllable adaptive algorithms based on a {Hessian} recovery},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1424--1434},
year = {2005},
volume = {45},
number = {8},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_8_a7/}
}
TY - JOUR AU - Yu. V. Vassilevski AU - K. N. Lipnikov TI - Error bounds for controllable adaptive algorithms based on a Hessian recovery JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2005 SP - 1424 EP - 1434 VL - 45 IS - 8 UR - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_8_a7/ LA - ru ID - ZVMMF_2005_45_8_a7 ER -
%0 Journal Article %A Yu. V. Vassilevski %A K. N. Lipnikov %T Error bounds for controllable adaptive algorithms based on a Hessian recovery %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2005 %P 1424-1434 %V 45 %N 8 %U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_8_a7/ %G ru %F ZVMMF_2005_45_8_a7
Yu. V. Vassilevski; K. N. Lipnikov. Error bounds for controllable adaptive algorithms based on a Hessian recovery. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 8, pp. 1424-1434. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_8_a7/
[1] D'Azevedo E., “Optimal triangular mesh generation by coordinate transformation”, SIAM J. Sci. Stat. Comput., 12:4 (1991), 755–786 | DOI | MR
[2] Rippa S., “Long and thin triangles can be good for linear interpolation”, SIAM J. Numer. Anal., 29 (1992), 257–270 | DOI | MR | Zbl
[3] Agouzal A., Lipnikov K., Vassilevski Y., “Adaptive generation of quasi-optimal tetrahedral meshes”, East-West J. Numer. Math., 7:4 (1999), 223–244 | MR | Zbl
[4] Agouzal A., Vassilevski Y., “On a discrete Hessian recovery for $P_1$ finite elements”, J. Numer. Math., 10:1 (2002), 1–12 | DOI | MR | Zbl
[5] Buscaglia G., Dari E., “Anisotropic mesh optimization and its application in adaptivity”, Internat. J. Numer. Meth. Engng., 40 (1997), 4119–4136 | 3.0.CO;2-R class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | Zbl
[6] Buscaglia G., Agouzal A., Ramirez P., Dari E., “On Hessian recovery and anisotropic adaptivity”, Proc. ECCOMAS 98, Athens, Greece, 1998, 403–407
[7] Zienkiewicz O., Wu J., “Automatic directional refinement in adaptive analysis of compressible flows”, Internat. J. Numer. Meth. Engnr., 37 (1994), 2189–2210 | DOI | MR | Zbl
[8] Apel T., Randrianarivony H., “Stability of discretizations of the Stokes problem on anisotropic meshes”, Math. Comput. Simulat., 61 (2003), 437–447 | DOI | MR | Zbl
[9] Prudhomme S., Oden J., “On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors”, Comput. Methods Appl. Mech. Engrg., 176 (1999), 313–331 | DOI | MR | Zbl
[10] Vassilevski Y., Lipnikov K., “Optimal triangulations: existence, approximation and double differentiation of $P_1$ finite element functions”, Comput. Math. and Math. Phys., 43:6 (2003), 827–835 | MR
[11] D'Azevedo E., Simpson R., “On optimal triangular meshes for minimizing the gradient error”, Numer. Math., 59 (1991), 321–348 | DOI | MR
[12] Zavattieri P., Dari E., Buscaglia G., “Optimization strategies in unstructured mesh generation”, Internat. J. Numer. Meth. Engng., 39 (1996), 2055–2071 | 3.0.CO;2-2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | Zbl
[13] Vassilevski Y., Lipnikov K., “Adaptive algorithm for generation of quasi-optimal meshes”, Comput. Math. and Math. Phys., 39:9 (1999), 1532–1551 | MR
[14] Ciarlet P. G., Wagschal C., “Multipoint Taylor formulas and applications to the finite element method”, Numer. Math., 17 (1971), 84–100 | DOI | MR | Zbl
[15] Ciarlet P. G., The finite element method for elliptic problems, North-Holland, Amsterdam, 1978 | MR | Zbl
[16] Lipnikov K., Vassilevski Y., “On control of adaptation in parallel mesh generation”, Engng. Comput., 20:3 (2004), 193–201 | DOI
[17] Lipnikov K., Vassilevski Y., “Parallel adaptive solution of 3D boundary value problems by Hessian recovery”, Comput. Meth. Appl. Mech. Engng., 192:11–12 (2003), 1495–1513 | DOI | MR | Zbl
[18] Apel T., Anisotropic finite elements: Local estimates and applications, Teubner, Stuttgart, 1999 | MR | Zbl