Uniform discrete Sobolev estimates of solutions to finite difference schemes for singular limits of nonlinear PDEs
1 Department of Mathematics and Computer Science, Open University, 43107 Raanana, Israel.
2 School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel.
Received: 9 July 2015
Revised: 7 February 2016
Accepted: 16 May 2016
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.
Mathematics Subject Classification: 65M10
Key words: Uniform estimates / finite-difference methods / discrete Sobolev spaces / fully-discrete sharp Gårding inequality / singular limits
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