Uniform discrete Sobolev estimates of solutions to finite difference schemes for singular limits of nonlinear PDEs

L Mandel, Steven Schochet

Type: Article

Publication Date: 2016-05-24

Citations: 3

DOI: https://doi.org/10.1051/m2an/2016038

Abstract

Uniform discrete Sobolev space estimates are proven for a class of finite-difference schemes for singularly-perturbed hyperbolic-parabolic systems. The estimates obtained improve previous results even when the PDEs do not involve singular perturbations. These estimates are used in a companion paper to prove the convergence of solutions as the discretization parameter and/or the singular perturbation parameter tends to zero.

Locations

ESAIM Mathematical Modelling and Numerical Analysis - View
French digital mathematics library (Numdam) - View - PDF

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