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

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.