A divergence‐conforming method for flow and double‐diffusive transport

Abstract

The results of a recent extension of the analysis of an ‐conforming method for a model of double‐diffusive flow in porous media introduced in [Bürger, Méndez, Ruiz‐Baier, SINUM (2019), 57:1318–1343] to the time‐dependent case are summarized. These include the efficiency and reliability of residual‐based a posteriori error estimators for the steady, semi‐discrete, and fully discrete problems. The method consists of Brezzi–Douglas–Marini approximations for velocity and compatible piecewise discontinuous pressures, whereas Lagrangian elements are used for concentration and salinity. Novel numerical tests confirm the accuracy of the method and illustrate its application to a salinity‐driven problem of sedimentation.