Divergence-conforming methods for transient doubly-diffusive flows: A priori and a posteriori error analysis

02/11/2021 ∙ by Raimund Bürger, et al. ∙ 0

The analysis of the double-diffusion model and 𝐇(div)-conforming method introduced in [Bürger, Méndez, Ruiz-Baier, SINUM (2019), 57:1318–1343] is extended to the time-dependent case. In addition, the efficiency and reliability analysis of residual-based a posteriori error estimators for the steady, semi-discrete, and fully discrete problems is established. The resulting methods are applied to simulate the sedimentation of small particles in salinity-driven flows. The method consists of Brezzi-Douglas-Marini approximations for velocity and compatible piecewise discontinuous pressures, whereas Lagrangian elements are used for concentration and salinity distribution. Numerical tests confirm the properties of the proposed family of schemes and of the adaptive strategy guided by the a posteriori error indicators.



There are no comments yet.


page 28

page 29

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.