A new optimization-based numerical method is proposed for the solution to diffusion problems with sign-changing conductivity coefficients. In contrast to existing approaches, our method does not rely on the discretization of a stabilized equation, and the convergence of the scheme can be proved without any symmetry assumption on the mesh near the interface where the conductivity sign changes.
Nous proposons une nouvelle méthode, basée sur la résolution d'un problème de minimisation, pour l'approximation de problèmes de diffusion avec changement de signe. Cette approche, qui tire profit d'une reformulation du modèle initial sous la forme d'un problème de transmission, ne repose pas sur la discrétisation d'une équation stabilisée, et la convergence de la méthode est obtenue sans hypothèse de symétrie du maillage dans un voisinage de l'interface où la conductivité change de signe.
Accepted:
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@article{CRMATH_2017__355_4_472_0, author = {Abdulle, Assyr and Huber, Martin E. and Lemaire, Simon}, title = {An optimization-based numerical method for diffusion problems with sign-changing coefficients}, journal = {Comptes Rendus. Math\'ematique}, pages = {472--478}, publisher = {Elsevier}, volume = {355}, number = {4}, year = {2017}, doi = {10.1016/j.crma.2017.02.010}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2017.02.010/} }
TY - JOUR AU - Abdulle, Assyr AU - Huber, Martin E. AU - Lemaire, Simon TI - An optimization-based numerical method for diffusion problems with sign-changing coefficients JO - Comptes Rendus. Mathématique PY - 2017 SP - 472 EP - 478 VL - 355 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.02.010/ DO - 10.1016/j.crma.2017.02.010 LA - en ID - CRMATH_2017__355_4_472_0 ER -
%0 Journal Article %A Abdulle, Assyr %A Huber, Martin E. %A Lemaire, Simon %T An optimization-based numerical method for diffusion problems with sign-changing coefficients %J Comptes Rendus. Mathématique %D 2017 %P 472-478 %V 355 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.02.010/ %R 10.1016/j.crma.2017.02.010 %G en %F CRMATH_2017__355_4_472_0
Abdulle, Assyr; Huber, Martin E.; Lemaire, Simon. An optimization-based numerical method for diffusion problems with sign-changing coefficients. Comptes Rendus. Mathématique, Volume 355 (2017) no. 4, pp. 472-478. doi : 10.1016/j.crma.2017.02.010. http://www.numdam.org/articles/10.1016/j.crma.2017.02.010/
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