In this paper we show unique solvability of an abstract coupled problem which originates from a field/circuit coupled problem. The coupled problem arises in particular from modified nodal analysis equations linked with an eddy current problem via solid conductor model. The proof technique in the paper relies on Rothe’s method and the theory of monotone operator. We also provide error estimates for time discretization.
Accepté le :
DOI : 10.1051/m2an/2016052
Mots clés : Coupled problem, field/circuit, uniqueness, convergence, time discretization
@article{M2AN_2017__51_3_1045_0,
author = {Slodi\v{c}ka, Marian and Vr\'abel{\textquoteright}, Vladim{\'\i}r},
title = {Existence and uniqueness of a solution for a field/circuit coupled problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1045--1061},
publisher = {EDP-Sciences},
volume = {51},
number = {3},
year = {2017},
doi = {10.1051/m2an/2016052},
zbl = {1384.78010},
mrnumber = {3666656},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2016052/}
}
TY - JOUR AU - Slodička, Marian AU - Vrábel’, Vladimír TI - Existence and uniqueness of a solution for a field/circuit coupled problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1045 EP - 1061 VL - 51 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016052/ DO - 10.1051/m2an/2016052 LA - en ID - M2AN_2017__51_3_1045_0 ER -
%0 Journal Article %A Slodička, Marian %A Vrábel’, Vladimír %T Existence and uniqueness of a solution for a field/circuit coupled problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1045-1061 %V 51 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016052/ %R 10.1051/m2an/2016052 %G en %F M2AN_2017__51_3_1045_0
Slodička, Marian; Vrábel’, Vladimír. Existence and uniqueness of a solution for a field/circuit coupled problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 3, pp. 1045-1061. doi : 10.1051/m2an/2016052. http://www.numdam.org/articles/10.1051/m2an/2016052/
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