Naslov
Monotone Numerical Schemes for a Dirichlet problem for Elliptic Operators in Divergence Form

Autori
Rogina, Mladen ; Limić, Nedžad

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
ICNAAM International Conference on Numerical Analysis and Applied Mathematics 2006 / Simos, T. E. ; Psihoyios G. ; Tsitouras, Ch. - Weinheim : Wiley-VCH, 2006, 279-282

Skup
ICNAAM International Conference on Numerical Analysis and Applied Mathematics 2006

Mjesto i datum
Hersonissos, Grčka, 15.09.2006. - 19.09.2006

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Dirichlet problem; elliptic operators; divergence form

Sažetak
The object of present analysis are numerical solutions of the elliptic boundary value problems in terms of monotone schemes. We assume that the elliptic differential operator has the divergence form, with measurable coefficients satisfying the strict ellipticity condition. The basic idea of monotone schemes can be found in [6] without the analysis of convergence of approximate solutions. Convergence proofs for $C$ spaces can be found in [9], and for $L_1(\mathbb{; ; R}; ; ^d)$-spaces in [4] with the restriction on dimension ($d = 2$ and $d = 3$) ; an extension for $d > 3$ can be found in [5]. Here we consider schemes possessing stencils enclosed by rectangles with vertices at grid-knots, and extend published results by constructing schemes with stencils stretching far from basic grid-rectangles, so being conceptually closer to the original idea in [6]. The schemes are not derived from finite difference operators approximating differential operators, but rather from a general principle which ensures the convergence of approximate solutions. In the case of the classical elliptic problem, this general principle is necessary and sufficient to prove convergence in H\"{; ; o}; ; lder spaces.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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