Multipliers in Sobolev spaces and exact convergence rate estimates for the finite-difference schemes

Boško Jovanović

Banach Center Publications (1994)

  • Volume: 29, Issue: 1, page 165-173
  • ISSN: 0137-6934

Abstract

top
In this paper we present some recent results concerning convergence rate estimates for finite-difference schemes approximating boundary-value problems. Special attention is given to the problem of minimal smoothness of coefficients in partial differential equations necessary for obtaining the results.

How to cite

top

Jovanović, Boško. "Multipliers in Sobolev spaces and exact convergence rate estimates for the finite-difference schemes." Banach Center Publications 29.1 (1994): 165-173. <http://eudml.org/doc/262749>.

@article{Jovanović1994,
abstract = {In this paper we present some recent results concerning convergence rate estimates for finite-difference schemes approximating boundary-value problems. Special attention is given to the problem of minimal smoothness of coefficients in partial differential equations necessary for obtaining the results.},
author = {Jovanović, Boško},
journal = {Banach Center Publications},
keywords = {finite differences; multipliers; boundary-value problems; Sobolev spaces; covergence; finite difference schemes; self-adjoint second order elliptic equations; rectangular grids; error analysis},
language = {eng},
number = {1},
pages = {165-173},
title = {Multipliers in Sobolev spaces and exact convergence rate estimates for the finite-difference schemes},
url = {http://eudml.org/doc/262749},
volume = {29},
year = {1994},
}

TY - JOUR
AU - Jovanović, Boško
TI - Multipliers in Sobolev spaces and exact convergence rate estimates for the finite-difference schemes
JO - Banach Center Publications
PY - 1994
VL - 29
IS - 1
SP - 165
EP - 173
AB - In this paper we present some recent results concerning convergence rate estimates for finite-difference schemes approximating boundary-value problems. Special attention is given to the problem of minimal smoothness of coefficients in partial differential equations necessary for obtaining the results.
LA - eng
KW - finite differences; multipliers; boundary-value problems; Sobolev spaces; covergence; finite difference schemes; self-adjoint second order elliptic equations; rectangular grids; error analysis
UR - http://eudml.org/doc/262749
ER -

References

top
  1. [1] R. A. Adams, Sobolev Spaces, Academic Press, New York 1975. 
  2. [2] J. H. Bramble and S. R. Hilbert, Bounds for a class of linear functionals with application to Hermite interpolation, Numer. Math. 16 (1971), 362-369. Zbl0214.41405
  3. [3] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam 1978. Zbl0383.65058
  4. [4] T. Dupont and R. Scott, Polynomial approximation of functions in Sobolev spaces, Math. Comp. 34 (1980), 441-463. Zbl0423.65009
  5. [5] B. S. Jovanović, On the convergence of finite-difference schemes for parabolic equations with variable coefficients, Numer. Math. 54 (1989), 395-404. Zbl0668.65069
  6. [6] B. S. Jovanović, Optimal error estimates for finite-difference schemes with variable coefficients, Z. Angew. Math. Mech. 70 (1990), 640-642. Zbl0715.65082
  7. [7] B. S. Jovanović, Convergence of finite-difference schemes for parabolic equations with variable coefficients, ibid. 71 (1991), 647-650. 
  8. [8] B. S. Jovanović, Convergence of finite-difference schemes for hyperbolic equations with variable coefficients, ibid. 72 (1992), to appear. Zbl0763.65075
  9. [9] B. S. Jovanović, L. D. Ivanović and E. E. Süli, Convergence of a finite-difference scheme for second-order hyperbolic equations with variable coefficients, IMA J. Numer. Anal. 7 (1987), 39-45. Zbl0624.65095
  10. [10] B. S. Jovanović, L. D. Ivanović and E. E. Süli, Convergence of finite-difference schemes for elliptic equations with variable coefficients, ibid., 301-305. Zbl0636.65096
  11. [11] R. D. Lazarov, On the question of convergence of finite-difference schemes for generalized solutions of the Poisson equation, Differentsial'nye Uravneniya 17 (1981), 1285-1294 (in Russian). 
  12. [12] R. D. Lazarov, V. L. Makarov and A. A. Samarskiĭ, Application of exact difference schemes for construction and investigation of difference schemes for generalized solutions, Mat. Sb. 117 (1982), 469-480 (in Russian). Zbl0494.65055
  13. [13] R. D. Lazarov, V. L. Makarov and W. Weinelt, On the convergence of difference schemes for the approximation of solutions u W 2 m (m > 0.5) of elliptic equations with mixed derivatives, Numer. Math. 44 (1984), 223-232. Zbl0525.65069
  14. [14] V. G. Maz'ya and T. O. Shaposhnikova, Theory of Multipliers in Spaces of Differentiable Functions, Monographs Stud. Math. 23, Pitman, Boston 1985. 
  15. [15] A. A. Samarskiĭ, Theory of Difference Schemes, Nauka, Moscow 1983 (in Russian). 
  16. [16] E. Süli, B. Jovanović and L. Ivanović, Finite difference approximations of generalized solutions, Math. Comp. 45 (1985), 319-327. Zbl0586.65064
  17. [17] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Deutscher Verlag der Wissenschaften, Berlin 1978. Zbl0387.46033
  18. [18] J. Wloka, Partial Differential Equations, Cambridge Univ. Press, 1987. Zbl0623.35006

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.