Convergence of solutions to finite difference schemes for singular limits of nonlinear evolutionary PDEs

Solutions of certain finite-difference schemes for singularly-perturbed evolutionary PDEs converge as the perturbation parameter and/or the discretization parameters tend to zero. Under suitable hypotheses a sharp convergence rate of order one-half in the time step, uniform in the perturbation param...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2017-03, Vol.51 (2), p.587-614
Main Authors: Even-Dar Mandel, L., Schochet, S.
Format: Article
Language:English
Subjects:
65M12
Convergence
discrete Sobolev spaces
Finite difference method
Parameters
Perturbation
Rate of convergence
singular limits
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Description
Summary:Solutions of certain finite-difference schemes for singularly-perturbed evolutionary PDEs converge as the perturbation parameter and/or the discretization parameters tend to zero. Under suitable hypotheses a sharp convergence rate of order one-half in the time step, uniform in the perturbation parameter, is obtained.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2016029