Solutions of certain finite-difference schemes for singularly-perturbed evolutionary PDEs converge as the perturbation parameter and/or the discretization parameters tend to zero. Under suitable hypotheses a sharp convergence rate of order one-half in the time step, uniform in the perturbation parameter, is obtained.
Accepté le :
DOI : 10.1051/m2an/2016029
Keywords: Rate of convergence, discrete Sobolev spaces, singular limits
Even-Dar Mandel, L. 1 ; Schochet, S. 1
@article{M2AN_2017__51_2_587_0,
author = {Even-Dar Mandel, L. and Schochet, S.},
title = {Convergence of solutions to finite difference schemes for singular limits of nonlinear evolutionary {PDEs}},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {587--614},
year = {2017},
publisher = {EDP Sciences},
volume = {51},
number = {2},
doi = {10.1051/m2an/2016029},
mrnumber = {3626412},
zbl = {1368.65158},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2016029/}
}
TY - JOUR AU - Even-Dar Mandel, L. AU - Schochet, S. TI - Convergence of solutions to finite difference schemes for singular limits of nonlinear evolutionary PDEs JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 587 EP - 614 VL - 51 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2016029/ DO - 10.1051/m2an/2016029 LA - en ID - M2AN_2017__51_2_587_0 ER -
%0 Journal Article %A Even-Dar Mandel, L. %A Schochet, S. %T Convergence of solutions to finite difference schemes for singular limits of nonlinear evolutionary PDEs %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 587-614 %V 51 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2016029/ %R 10.1051/m2an/2016029 %G en %F M2AN_2017__51_2_587_0
Even-Dar Mandel, L.; Schochet, S. Convergence of solutions to finite difference schemes for singular limits of nonlinear evolutionary PDEs. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 587-614. doi: 10.1051/m2an/2016029
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