• Home
  • UCSC journals portal
  • ANID repository
  • UCSC Thesis Repository
  • English
  • Español
  • Log In
    Have you forgotten your password?
  1. Home
  2. Productividad Científica
  3. Publicaciones Científicas
  4. Residual-based a posteriori error analysis for the coupling of the Navier–Stokes and Darcy–Forchheimer equations
 
Options
Residual-based a posteriori error analysis for the coupling of the Navier–Stokes and Darcy–Forchheimer equations
Dr. Caucao-Paillán, Sergio 
Facultad de Ingeniería 
Gatica, Gabriel
Oyarzúa, Ricardo
Sandoval, Felipe
10.1051/m2an/2021005
EDP Sciences
2021
In this paper we consider a mixed variational formulation that have been recently proposed for the coupling of the Navier–Stokes and Darcy–Forchheimer equations, and derive, though in a non-standard sense, a reliable and efficient residual-baseda posteriorierror estimator suitable for an adaptive mesh-refinement method. For the reliability estimate, which holds with respect to the square root of the error estimator, we make use of the inf-sup condition and the strict monotonicity of the operators involved, a suitable Helmholtz decomposition in non-standard Banach spaces in the porous medium, local approximation properties of the Clément interpolant and Raviart–Thomas operator, and a smallness assumption on the data. In turn, inverse inequalities, the localization technique based on triangle-bubble and edge-bubble functions in localLpspaces, are the main tools for developing the efficiency analysis, which is valid for the error estimator itself up to a suitable additional error term. Finally, several numerical results confirming the properties of the estimator and illustrating the performance of the associated adaptive algorithm are reported.
Thumbnail Image
Download
Name

Residual-based a posteriori error analysis for the coupling of the Navier–Stokes and Darcy–Forchheimer equations.pdf

Size

1.51 MB

Format

Checksum
65N30
65N12
65N15
35Q79
80A20
76R05
76D07
Historial de mejoras
Proyecto financiado por: