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

Even-Dar Mandel, Liat; Schochet, Steven

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 727-757.

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.

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