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

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

The analysis of the double-diffusion model and 𝐇(div)-conforming method introduced in [BĂŒrger, MĂ©ndez, 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.

READ FULL TEXT

page 28

page 29

research
∙ 01/10/2022

A posteriori analysis for a mixed FEM discretization of the linear elasticity spectral problem

In this paper we analyze a posteriori error estimates for a mixed formul...
research
∙ 03/01/2022

A posteriori error analysis for approximations of time-fractional subdiffusion problems

In this paper we consider a sub-diffusion problem where the fractional t...
research
∙ 04/15/2020

A posteriori error analysis of a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations

A local adaptive discontinuous Galerkin method for convection-diffusion-...
research
∙ 12/29/2022

A posteriori error analysis and adaptivity for a VEM discretization of the Navier-Stokes equations

We consider the Virtual Element method (VEM) introduced by BeirĂŁo da Vei...
research
∙ 04/13/2021

Parallelized Discrete Exterior Calculus for Three-Dimensional Elliptic Problems

A formulation of elliptic boundary value problems is used to develop the...
research
∙ 01/23/2020

Goal-oriented a posteriori estimation of numerical errors in the solution of multiphysics systems

This paper develops a general methodology for a posteriori error estimat...

Please sign up or login with your details

Forgot password? Click here to reset