# 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

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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

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- [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 $u\in {W}_{2}^{m}$ (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

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