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This paper provides an equivalent characterization of the discrete maximum principle for Galerkin solutions of general linear elliptic problems. The characterization is formulated in terms of the discrete Green’s function and the elliptic projection of the boundary data. This general concept is applied to the analysis of the discrete maximum principle for the higher-order finite elements in one-dimension and to the lowest-order finite elements on simplices of arbitrary dimension. The paper surveys...
This paper is devoted to some nonlinear propagation phenomena in periodic and more
general domains, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a
follow-up of the article [7]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of the domain,...
The numerical solution of the elliptic Monge-Ampère Partial Differential
Equation has been a subject of increasing interest recently [Glowinski,
in 6th International
Congress on Industrial and Applied Mathematics, ICIAM 07, Invited Lectures (2009) 155–192;
Oliker and Prussner,
Numer. Math.54 (1988) 271–293; Oberman,
Discrete Contin. Dyn. Syst. Ser. B10 (2008) 221–238; Dean and Glowinski,
in Partial differential equations, Comput.
Methods Appl. Sci. 16 (2008) 43–63; Glowinski et al.,
Japan...
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