Geodesic
Uniform discrete Sobolev estimates of solutions to finite difference schemes for singular limits of nonlinear PDEs
Even-Dar Mandel, Liat1, 2 ; Schochet, Steven2
1 Department of Mathematics and Computer Science, Open University, 43107 Raanana, Israel.
2 School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 727-757

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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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016038
Classification : 65M10
Keywords: Uniform estimates, finite-difference methods, discrete Sobolev spaces, fully-discrete sharp Gårding inequality, singular limits

Even-Dar Mandel, Liat 1, 2 ; Schochet, Steven 2

1 Department of Mathematics and Computer Science, Open University, 43107 Raanana, Israel.
2 School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel. 
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     title = {Uniform discrete {Sobolev} estimates of solutions to finite difference schemes for singular limits of nonlinear {PDEs}},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {727--757},
     publisher = {EDP-Sciences},
     volume = {51},
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Even-Dar Mandel, Liat; Schochet, Steven. Uniform discrete Sobolev estimates of solutions to finite difference schemes for singular limits of nonlinear PDEs. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 727-757. doi: 10.1051/m2an/2016038

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