In this paper we analyze the large-time behavior of the augmented Burgers equation. We first study the well-posedness of the Cauchy problem and obtain - decay rates. The asymptotic behavior of the solution is obtained by showing that the influence of the convolution term is the same as for large times. Then, we propose a semi-discrete numerical scheme that preserves this asymptotic behavior, by introducing two correcting factors in the discretization of the non-local term. Numerical experiments illustrating the accuracy of the results of the paper are also presented.
Accepté le :
DOI : 10.1051/m2an/2017029
Mots clés : Augmented Burgers equation, numerical approximation, large-time behavior
@article{M2AN_2017__51_6_2367_0, author = {Ignat, Liviu I. and Pozo, Alejandro}, title = {A semi-discrete large-time behavior preserving scheme for the augmented {Burgers} equation}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {2367--2398}, publisher = {EDP-Sciences}, volume = {51}, number = {6}, year = {2017}, doi = {10.1051/m2an/2017029}, mrnumber = {3745175}, zbl = {1394.65089}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2017029/} }
TY - JOUR AU - Ignat, Liviu I. AU - Pozo, Alejandro TI - A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 2367 EP - 2398 VL - 51 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017029/ DO - 10.1051/m2an/2017029 LA - en ID - M2AN_2017__51_6_2367_0 ER -
%0 Journal Article %A Ignat, Liviu I. %A Pozo, Alejandro %T A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 2367-2398 %V 51 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017029/ %R 10.1051/m2an/2017029 %G en %F M2AN_2017__51_6_2367_0
Ignat, Liviu I.; Pozo, Alejandro. A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2367-2398. doi : 10.1051/m2an/2017029. http://www.numdam.org/articles/10.1051/m2an/2017029/
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