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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 8, Pages 1424–1434 (Mi zvmmf612)  

This article is cited in 5 scientific papers (total in 5 papers)

Error bounds for controllable adaptive algorithms based on a Hessian recovery

Yu. V. Vassilevskia, K. N. Lipnikovb

a Institute of Numerical Mathematics, Russian Academy of Sciences
b Los Alamos National Laboratory, MS B284, Los Alamos, NM, 87545, USA

Abstract: One of the main goals of adaptive algorithms for unstructured mesh generation is to obtain a better discretization error with the use of the least possible number of mesh cells. For many problems, the discretization error can be bounded above by the interpolation error. The main goal of this paper is to analyze the interpolation error for controllable adaptive algorithms based on a Hessian recovery.

Key words: algorithms for adaptive mesh generation, interpolation-error estimates, control of adaptation.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:8, 1374–1384

Bibliographic databases:
UDC: 519.63
Received: 05.11.2004

Citation: Yu. V. Vassilevski, K. N. Lipnikov, “Error bounds for controllable adaptive algorithms based on a Hessian recovery”, Zh. Vychisl. Mat. Mat. Fiz., 45:8 (2005), 1424–1434; Comput. Math. Math. Phys., 45:8 (2005), 1374–1384

Citation in format AMSBIB
\Bibitem{VasLip05}
\by Yu.~V.~Vassilevski, K.~N.~Lipnikov
\paper Error bounds for controllable adaptive algorithms based on a Hessian recovery
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 8
\pages 1424--1434
\mathnet{http://mi.mathnet.ru/zvmmf612}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2191854}
\zmath{https://zbmath.org/?q=an:1087.65113}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 8
\pages 1374--1384


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Jensen K.E., Gorman G., “Details of Tetrahedral Anisotropic Mesh Adaptation”, Comput. Phys. Commun., 201 (2016), 135–143  crossref  zmath  isi  scopus
    2. Mesri Y., Khalloufi M., Hachem E., “On optimal simplicial 3D meshes for minimizing the Hessian-based errors”, Appl. Numer. Math., 109 (2016), 235–249  crossref  mathscinet  zmath  isi  elib  scopus
    3. Brethes G., Dervieux A., “Anisotropic norm-oriented mesh adaptation for a Poisson problem”, J. Comput. Phys., 322 (2016), 804–826  crossref  mathscinet  zmath  isi  elib  scopus
    4. Jensen K.E., “Topology Optimization of Stokes Flow on Dynamic Meshes Using Simple Optimizers”, Comput. Fluids, 174 (2018), 66–77  crossref  mathscinet  zmath  isi  scopus
    5. Loseille A., Frazza L., Alauzet F., “Comparing Anisotropic Adaptive Strategies on the Second AIAA Sonic Boom Workshop Geometry”, J. Aircr., 56:3 (2019), 938–952  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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