Multipliers in Sobolev spaces and exact convergence rate estimates for the finite-difference schemes
Banach Center Publications (1994)
- Volume: 29, Issue: 1, page 165-173
- ISSN: 0137-6934
Access Full Article
topAbstract
topHow to cite
topJovanović, 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] R. A. Adams, Sobolev Spaces, Academic Press, New York 1975.
- [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] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam 1978. Zbl0383.65058
- [4] T. Dupont and R. Scott, Polynomial approximation of functions in Sobolev spaces, Math. Comp. 34 (1980), 441-463. Zbl0423.65009
- [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] B. S. Jovanović, Optimal error estimates for finite-difference schemes with variable coefficients, Z. Angew. Math. Mech. 70 (1990), 640-642. Zbl0715.65082
- [7] B. S. Jovanović, Convergence of finite-difference schemes for parabolic equations with variable coefficients, ibid. 71 (1991), 647-650.
- [8] B. S. Jovanović, Convergence of finite-difference schemes for hyperbolic equations with variable coefficients, ibid. 72 (1992), to appear. Zbl0763.65075
- [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] 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] 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] 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] R. D. Lazarov, V. L. Makarov and W. Weinelt, On the convergence of difference schemes for the approximation of solutions (m > 0.5) of elliptic equations with mixed derivatives, Numer. Math. 44 (1984), 223-232. Zbl0525.65069
- [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] A. A. Samarskiĭ, Theory of Difference Schemes, Nauka, Moscow 1983 (in Russian).
- [16] E. Süli, B. Jovanović and L. Ivanović, Finite difference approximations of generalized solutions, Math. Comp. 45 (1985), 319-327. Zbl0586.65064
- [17] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Deutscher Verlag der Wissenschaften, Berlin 1978. Zbl0387.46033
- [18] J. Wloka, Partial Differential Equations, Cambridge Univ. Press, 1987. Zbl0623.35006
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.