Displaying similar documents to “A Multiscale Enrichment Procedure for Nonlinear Monotone Operators”

Numerical computation of solitons for optical systems

Laurent Di Menza (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large are large nonlinear exponents . In a second part,...

Finite volume schemes for fully non-linear elliptic equations in divergence form

Jérôme Droniou (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the -Laplacian kind: -div(|∇∇) = ƒ (with 1 < < ∞). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.