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Strong convergence of the numerical solution to a weak solution is proved for a nonlinear coupled flow and transport problem arising in porous media. The method combines a mixed finite element method for the pressure and velocity with an interior penalty discontinuous Galerkin method in space for the concentration. Using functional tools specific to broken Sobolev spaces, the convergence of the broken gradient of the numerical concentration to the weak solution is obtained in theL²norm. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 489–513, 2017

Understanding the behavior of lithium‐ion batteries (LIBs) under extreme conditions, for example, low temperature, is key to broad adoption of LIBs in various application scenarios. LIBs, poor performance at low temperatures is often attributed to the inferior lithium‐ion transport in the electrolyte, which has motivated new electrolyte development as well as the battery preheating approach that is popular in electric vehicles. A significant irrevocable capacity loss, however, is not resolved by these measures nor well understood. Herein, multiphase, multiscale chemomechanical behaviors in composite LiNi_xMn_yCo_zO₂(NMC,x +y +z = 1) cathodes at extremely low temperatures are systematically elucidated. The low‐temperature storage of LIBs can result in irreversible structural damage in active electrodes, which can negatively impact the subsequent battery cycling performance at ambient temperature. Beside developing electrolytes that have stable performance, designing batteries for use in a wide temperature range also calls for the development of electrode components that are structurally and morphologically robust when the cell is switched between different temperatures.