Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon

Douglas N. Arnold; L. Ridgway Scott; Michael Vogelius

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1988)

  • Volume: 15, Issue: 2, page 169-192
  • ISSN: 0391-173X

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Arnold, Douglas N., Scott, L. Ridgway, and Vogelius, Michael. "Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 15.2 (1988): 169-192. <http://eudml.org/doc/84028>.

@article{Arnold1988,
author = {Arnold, Douglas N., Scott, L. Ridgway, Vogelius, Michael},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {divergence operator; Dirichlet boundary value problem; polygonal domain},
language = {eng},
number = {2},
pages = {169-192},
publisher = {Scuola normale superiore},
title = {Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon},
url = {http://eudml.org/doc/84028},
volume = {15},
year = {1988},
}

TY - JOUR
AU - Arnold, Douglas N.
AU - Scott, L. Ridgway
AU - Vogelius, Michael
TI - Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1988
PB - Scuola normale superiore
VL - 15
IS - 2
SP - 169
EP - 192
LA - eng
KW - divergence operator; Dirichlet boundary value problem; polygonal domain
UR - http://eudml.org/doc/84028
ER -

References

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  1. [1] R.A. Adams, Sobolev Spaces, Academic Press, New York, NY, 1975. Zbl0314.46030MR450957
  2. [2] D.N. Arnold - F. Brezzi - J. Douglas, PEERS: A new mixed finite element for plane elasticity, Japan J. Appl. Math., 1 (1984), pp. 347-367. Zbl0633.73074MR840802
  3. [3] P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman, Marshfield, MA, 1985. Zbl0695.35060MR775683
  4. [4] G.N. Jakovlev, Traces of functions in the space Wl p on piecewise smooth surfaces, Mat. Sb. (N.S.), 74 (1967). Math. USSR-Sb., 3 (1967), pp. 481-497. Zbl0174.44004MR220053
  5. [5] J.L. Lions - E. Magenes, Non-homogeneous Boundary Value Problems and Applications, I, Springer-Verlag, New York-Heidelberg -Berlin, 1972. Zbl0223.35039
  6. [6] M. Morley, A family of mixed elements for linear elasticity, Univ. of Chicago, PhD Thesis, 1986. 
  7. [7] J Nečas, Les Méthodes Directes en Théorie des Équations Elliptiques, Masson et Cie., Paris, 1967. MR227584
  8. [8] L.R. Scott - M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials, Math. Modelling and Numer. Anal., 19 (1985), pp. 111-143. Zbl0608.65013MR813691
  9. [9] K.T. Smith, A Primer of Modern Analysis, Springer-Verlag, New York-Heidelberg-Berlin, 1983. Zbl0517.26001MR710655
  10. [10] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. Zbl0207.13501MR290095

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