Naslov
Monotone schemes for a class of nonlinear elliptic and parabolic problems

Autori
Limić, Nedžad ; Rogina, Mladen

Izvornik
Nonlinear analysis (1468-1218) 11 (2010), 6; 4546-4553

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
homogenization; elliptic operator; nonlinear parabolic PDE; divergence form; monotone scheme

Sažetak
We construct monotone numerical schemes for a class of nonlinear PDE for elliptic and initial value problems for parabolic problems. The elliptic part is closely connected to a linear elliptic operator, which we discretize by monotone schemes, and solve the nonlinear problem by iteration. We assume that the elliptic differential operator is in the divergence form, with measurable coefficients satisfying the strict ellipticity condition, and that the right-hand side is a positive Radon measure. The numerical schemes are not derived from finite difference operators approximating differential operators, but rather from a general principle which ensures the convergence of approximate solutions. The main feature of these schemes is that they possess stencils stretching far from basic grid-rectangles, thus leading to system matrices which are related to M-matrices.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA