The solution to the initial and Dirichlet boundary value problem for a semilinear, one dimensional heat equation is approximated by a numerical method that combines the Besse Relaxation Scheme in time [C. R. Acad. Sci. Paris Sér. I 326 (1998)] with a central finite difference method in space. A new, composite stability argument is developed, leading to an optimal, second-order error estimate in the discrete -norm at the time-nodes and in the discrete -norm at the intermediate time-nodes. It is the first time in the literature where the Besse Relaxation Scheme is applied and analysed in the context of parabolic equations.
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Publié le :
DOI : 10.1051/m2an/2020077
Keywords: Besse Relaxation Scheme, semilinear heat equation, finite differences, Dirichlet boundary conditions, optimal order error estimates
@article{M2AN_2021__55_1_301_0,
author = {Zouraris, Georgios E.},
title = {Error estimation of the {Besse} {Relaxation} {Scheme} for a semilinear heat equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {301--328},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {1},
doi = {10.1051/m2an/2020077},
mrnumber = {4216828},
zbl = {1491.65080},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2020077/}
}
TY - JOUR AU - Zouraris, Georgios E. TI - Error estimation of the Besse Relaxation Scheme for a semilinear heat equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 301 EP - 328 VL - 55 IS - 1 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2020077/ DO - 10.1051/m2an/2020077 LA - en ID - M2AN_2021__55_1_301_0 ER -
%0 Journal Article %A Zouraris, Georgios E. %T Error estimation of the Besse Relaxation Scheme for a semilinear heat equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 301-328 %V 55 %N 1 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2020077/ %R 10.1051/m2an/2020077 %G en %F M2AN_2021__55_1_301_0
Zouraris, Georgios E. Error estimation of the Besse Relaxation Scheme for a semilinear heat equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 1, pp. 301-328. doi: 10.1051/m2an/2020077
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