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.
Accepté le :
DOI : 10.1051/m2an/2016038
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
@article{M2AN_2017__51_2_727_0,
author = {Even-Dar Mandel, Liat and Schochet, Steven},
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},
year = {2017},
publisher = {EDP Sciences},
volume = {51},
number = {2},
doi = {10.1051/m2an/2016038},
mrnumber = {3626417},
zbl = {1368.65163},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2016038/}
}
TY - JOUR AU - Even-Dar Mandel, Liat AU - Schochet, Steven TI - Uniform discrete Sobolev estimates of solutions to finite difference schemes for singular limits of nonlinear PDEs JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 727 EP - 757 VL - 51 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2016038/ DO - 10.1051/m2an/2016038 LA - en ID - M2AN_2017__51_2_727_0 ER -
%0 Journal Article %A Even-Dar Mandel, Liat %A Schochet, Steven %T Uniform discrete Sobolev estimates of solutions to finite difference schemes for singular limits of nonlinear PDEs %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 727-757 %V 51 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2016038/ %R 10.1051/m2an/2016038 %G en %F M2AN_2017__51_2_727_0
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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