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

Liat Even-Dar Mandel, Steven Schochet

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)727-757
Number of pages31
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume51
Issue number2
DOIs
StatePublished - 1 Mar 2017

Keywords

  • Discrete Sobolev spaces
  • Finite-difference methods
  • Fully-discrete sharp Gårding inequality
  • Singular limits
  • Uniform estimates

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