Convergence of solutions to finite difference schemes for singular limits of nonlinear evolutionary PDEs
Even-Dar Mandel, L.1 ; Schochet, S.1
1 School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 587-614.

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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016029
Classification : 65M12
Mots-clés : Rate of convergence, discrete Sobolev spaces, singular limits
Even-Dar Mandel, L. 1 ; Schochet, S. 1

1 School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel 
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     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},
     publisher = {EDP-Sciences},
     volume = {51},
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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. http://www.numdam.org/articles/10.1051/m2an/2016029/

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