Discrete Sobolev spaces and regularity of elliptic difference schemes

Rob Stevenson

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1991)

  • Volume: 25, Issue: 5, page 607-640
  • ISSN: 0764-583X

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Stevenson, Rob. "Discrete Sobolev spaces and regularity of elliptic difference schemes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 25.5 (1991): 607-640. <http://eudml.org/doc/193642>.

@article{Stevenson1991,
author = {Stevenson, Rob},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {regularity of elliptic difference schemes; minimal regularity; elliptic finite difference schemes; discrete (fractional order) Sobolev spaces},
language = {eng},
number = {5},
pages = {607-640},
publisher = {Dunod},
title = {Discrete Sobolev spaces and regularity of elliptic difference schemes},
url = {http://eudml.org/doc/193642},
volume = {25},
year = {1991},
}

TY - JOUR
AU - Stevenson, Rob
TI - Discrete Sobolev spaces and regularity of elliptic difference schemes
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1991
PB - Dunod
VL - 25
IS - 5
SP - 607
EP - 640
LA - eng
KW - regularity of elliptic difference schemes; minimal regularity; elliptic finite difference schemes; discrete (fractional order) Sobolev spaces
UR - http://eudml.org/doc/193642
ER -

References

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  2. [2] J. P. AUBIN, Approximation of elliptic boundary-value problems, Wiley-Inter-scienee, New York, 1972. Zbl0248.65063MR478662
  3. [3] K. P. BUBE and J. C. STRIKWERDA, Interior regularity estimates for elliptic systems of difference equations, SIAM J. Numer. Anal. 20 (1983), 653-670. Zbl0561.65070MR708449
  4. [4] W. HACKBUSCH, Convergence of Multi-Grid Iterations Applied to Difference Equations, Math. Comp. 34 (1980), 425-440. Zbl0422.65020MR559194
  5. [5] W. HACKBUSCH, On the regularity of difference schemes, Ark. Mat (1981), 71-95. Zbl0462.65058MR625538
  6. [6] W. HACKBUSCH, Analysis of discretizations by the concept of discrete regularity. In : The Mathematics of Finite Elements and Applications IV-MAFELAP 1981 (J.R. Whiteman, ed.) 369-376, Academic Press, London, 1982. Zbl0531.65053
  7. [7] W. HACKBUSCH, On the regularity of difference schemes, Part II, Regularity estimates for linear and nonlinear problems, Ark. Mat 21 (1983), 3-28. Zbl0535.65071MR706637
  8. [8] W. HACKBUSCH, Multi-Grid Methods and Applications, Springer-Verlag, Berlin, 1985. Zbl0595.65106
  9. [9] W. HACKBUSCH, Theorie and Numerik elliptischer Differentialgleichungen, B. G. Teubner, Stuttgart, 1986. Zbl0609.65065
  10. [10] J. NEČAS, Sur la coercivité des formes sesquilinéaires, elliptiques, Rev. Roumaine Math. Pures Appl. 9 (1964), 47-69. Zbl0196.40701MR179457
  11. [11] E. M. STEIN, Singular Integrals and Differentiability Properties of Functions, Princeton Universty Press, Princeton, New Jersey, 1970. Zbl0207.13501MR290095
  12. [12] F. STUMMEL, Elliptische Differenzenoperatoren unter Dirichletrandbedingungen, Math. Z. 97 (1967), 169-211. Zbl0149.07202MR224302
  13. [13] V. THOMÉE, Elliptic Difference Operators and Dirichet's Problem, Contributions to Differential Equations 3 (1964), 301-324. Zbl0143.38304MR163444
  14. [14] V. THOMEE and B. WESTERGEN, Elliptic Difference Equations and Interior Regularity, Numer. Math. 11 (1968), 196-210. Zbl0159.38204MR224303
  15. [15] J. WLOKA, Partielle Differentialgleichungen, B. G. Teubner, Stuttgart, 1982. Zbl0482.35001MR652934

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