skript-mehrgitter-sander.bib 5.26 KB
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@Book{braess:2013,
author = {Dietrich Braess},
title = {Finite Elemente},
publisher = {Springer Verlag},
note = {(English translation available)},
year = {2013}
}
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@techreport{shewchuk:1994,
 author = {Shewchuk, Jonathan R},
 title = {An Introduction to the Conjugate Gradient Method Without the Agonizing Pain},
 year = {1994},
 publisher = {Carnegie Mellon University},
 address = {Pittsburgh, PA, USA},
}

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@TechReport{shewchuk:2002,
 author = {Jonathan R. Shewchuk},
 title = {What is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures},
 institution = {Department of Electrical Engineering and Computer Science, University of California at Berkeley},
 year = {2002}
}

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@Book{dahmen_reusken:2008,
 title = {Numerik für Ingenieure und Naturwissenschaftler},
 publisher = {Springer},
 year = {2008},
 author = {Wolfgang Dahmen and Arnold Reusken}
}
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@MastersThesis{stolzmann:2020,
 author = {Henrik Stolzmann},
 title = {Robuste Mehrgittermethoden in $H(\operatorname{div})$},
 school = {TU Dresden, Fakultät für Mathematik},
 year = {2020},
 type = {Masterarbeit}
}

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@Book{pissanetzky:1984,
 title = {Sparse Matrix Technology},
 publisher = {Academic Press},
 year = {1984},
 author = {Sergio Pissanetzky}
}

@Article{hestenes_stiefel:1952,
 author = {Magnus R. Hestenes and Eduard Stiefel},
 title = {Methods of Conjugate Gradients for Solving Linear Systems},
 journal = {Journal of Research of the National Bureau of Standards},
 year = {1952},
 volume = {49},
 pages = {409--436}
}
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@Book{hackbusch:1994,
 title = {Iterative Solution of Large Sparse Systems of Equations},
 publisher = {Springer},
 year = {1994},
 author = {Wolfgang Hackbusch}
}
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@Book{trottenberg_oosterlee_schueller:2001,
 title = {Multigrid},
 publisher = {Elsevier Academic Press},
 year = {2001},
 author = {Ulrich Trottenberg and Cornelis Oosterlee and Anton Schüller}
}

@Article{yserentant:1993,
 author = {Harry Yserentant},
 title = {Old and New Convergence Proofs for Multigrid Methods},
 journal = {Acta Numerica},
 year = {1993},
 pages = {285--326}
}

@Article{bank_dupont_yserentant:1988,
 author = {R.E. Bank and T. Dupont and Harry Yserentant},
 title = {The hierarchical basis multigrid method},
 journal = {Numerische Mathematik},
 year = {1988},
 volume = {52},
 pages = {427--458}
}
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@Book{smith_bjorstad_gropp:1996,
 title = {Domain Decomposition -- Parallel Multilevel Methods for Elliptic Partial Differential Equations},
 publisher = {Cambridge University Press},
 year = {1996},
 author = {Barry Smith and Petter Bj{\o}rstad and William Gropp}
}

@misc{bramble1993multigrid,
  title={Multigrid methods, Pitman Research Notes in Mathematical Sciences, vol. 294},
  author={Bramble, J. H.},
  year={1993}
}
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@article{xu:1992,
 author = {Jinchao Xu},
 title = {Iterative methods by space decomposition and subspace correction},
 journal = {SIAM Review},
 volume = {34},
 year = {1992},
 pages = {581--613}
}

@article{graeser_kornhuber:2009,
 author = {Carsten Gräser and Ralf Kornhuber},
 title = {Multigrid Methods for Obstacle Problems},
 journal = {Journal of Computational Mathematics},
 volume = {27},
 number = {1},
 year = {2009},
 pages = {1--44}
}
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@article{arnold1997preconditioning,
  title={{Preconditioning in $H$(div) and applications}},
  author={Arnold, D. N. and Falk, R. S. and Winther, R.},
  journal={Mathematics of computation},
  year={1997}
}

@article{arnold2000multigrid,
  title={{Multigrid in $H$(div) and $H$(curl)}},
  author={Arnold, D. N. and Falk, R. S. and Winther, R.},
  journal={Numerische Mathematik},
  year={2000}
}
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@PhdThesis{zaglmayr:2006,
 author = {Sabine Zaglmayr},
 title = "High Order Finite Element Methods for Electromagnetic Field Computation.",
 school = {},
 year = {2006},
 url = {http://www.numerik.math.tugraz.at/~zaglmayr/pub/szthesis.pdf},
}

@Article{hiptmair:2002,
 author = {Ralf Hiptmair},
 title = {Finite elements in computational electromagnetism},
 journal = {Acta Numerica},
 year = {2002},
 volume = {11},
 pages = {237--339},
 doi = {10.1017/S0962492902000041},
}
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@Book{girault_raviart:1986,
 title = {Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms},
 publisher = {Springer},
 year = {1986},
 author = {Vivette Girault and Pierre-Arnaud Raviart},
}

@article{nedelec:1980,
  title={Mixed finite elements in $\R^3$},
  author={Nédélec, J. C.},
  volume = {34},
  pages = {315--341},
  journal={Numerische Mathematik},
  year={1980}
}

@incollection{raviart_thomas:1977,
  title={A mixed finite element method for 2-nd order elliptic problems},
  author={Raviart, P. A. and Thomas, J. M.},
  booktitle={Mathematical aspects of finite element methods},
  year={1977}
}

@article{rognes_kirby_logg:2010,
  title={{Efficient assembly of $H$(div) and $H$(curl) conforming finite elements}},
  author={Rognes, M. E. and Kirby, R. C. and Logg, A.},
  journal={SIAM Journal on Scientific Computing},
  year={2010}
}

@article{hiptmair:1999,
  title={Canonical construction of finite elements},
  author={Ralf Hiptmair},
  journal={Mathematics of computation},
  year={1999}
}
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@Article{carstensen:1997,
 author = {Carsten Carstensen},
 title = {Domain Decomposition for a Non-smooth Convex Minimization Problem and its Application to Plasticity},
 journal = {Numer. Linear Algebra Appl.},
 year = {1997},
 volume = {4},
 number = {3},
 pages = {177--190}
}