In this paper, the eddy current problem in a two-dimensional conductor containing a crack is studied. The decomposition of the electric field into a piecewise regular part and a singular part deriving from scalar potentials localized at the crack tip and at the crack mouth is proved. At the crack mouth, the electric field is shown to have standard singularities inside the conductor, but presents a singularity outside the conductor that does not belong to the classical -space. Well-posedness of the -based model and the -formulation of combined potentials are proved and an un-gauged discretization of the latter formulation is discussed.
DOI: 10.1051/m2an/2014027
Mots-clés : Eddy current problems, domains with cracks, singularities of solutions
@article{M2AN_2015__49_1_141_0, author = {Lohrengel, Stephanie and Nicaise, Serge}, title = {Analysis of eddy current formulations in two-dimensional domains with cracks}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {141--170}, publisher = {EDP-Sciences}, volume = {49}, number = {1}, year = {2015}, doi = {10.1051/m2an/2014027}, mrnumber = {3342195}, zbl = {1312.35037}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2014027/} }
TY - JOUR AU - Lohrengel, Stephanie AU - Nicaise, Serge TI - Analysis of eddy current formulations in two-dimensional domains with cracks JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 141 EP - 170 VL - 49 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014027/ DO - 10.1051/m2an/2014027 LA - en ID - M2AN_2015__49_1_141_0 ER -
%0 Journal Article %A Lohrengel, Stephanie %A Nicaise, Serge %T Analysis of eddy current formulations in two-dimensional domains with cracks %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 141-170 %V 49 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014027/ %R 10.1051/m2an/2014027 %G en %F M2AN_2015__49_1_141_0
Lohrengel, Stephanie; Nicaise, Serge. Analysis of eddy current formulations in two-dimensional domains with cracks. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 49 (2015) no. 1, pp. 141-170. doi : 10.1051/m2an/2014027. http://www.numdam.org/articles/10.1051/m2an/2014027/
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