%0 Journal Article %T Implicit discretization of Lagrangian gas dynamics %+ DAM Île-de-France (DAM/DIF) %+ Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)) %+ Laboratoire en Informatique Haute Performance pour le Calcul et la simulation (LIHPC) %+ Institut Universitaire de France (IUF) %A Plessier, Alexiane %A del Pino, Stéphane %A Després, Bruno %< avec comité de lecture %@ 2822-7840 %J ESAIM: Mathematical Modelling and Numerical Analysis %I Société de Mathématiques Appliquées et Industrielles (SMAI) %V 57 %N 2 %P 717-743 %8 2023-03 %D 2023 %R 10.1051/m2an/2022102 %K Implicit finite volume scheme %K Lagrangian formalism %K Entropy stability %K Convex analysis %Z Mathematics [math]Journal articles %X We construct an original framework based on convex analysis to prove the existence and uniqueness of a solution to a class of implicit numerical schemes. We propose an application of this general framework in the case of a new non linear implicit scheme for the 1D Lagrangian gas dynamics equations. We provide numerical illustrations that corroborate our proof of unconditional stability for this non linear implicit scheme. %G English %2 https://hal.science/hal-04048418v4/document %2 https://hal.science/hal-04048418v4/file/m2an220121.pdf %L hal-04048418 %U https://hal.science/hal-04048418 %~ CEA %~ CNRS %~ INSMI %~ LJLL %~ DAM %~ CEA-UPSAY %~ UNIV-PARIS-SACLAY %~ SORBONNE-UNIVERSITE %~ SORBONNE-UNIV %~ SU-SCIENCES %~ UNIV-PARIS %~ UNIVERSITE-PARIS %~ UP-SCIENCES %~ UNIVERSITE-PARIS-SACLAY %~ SU-TI %~ ALLIANCE-SU