A mixed-primal finite element method for the Boussinesq problem with temperature-dependent viscosity

DOI10.1007/s10092-018-0278-zzbMath1404.65248OpenAlexW2887800118MaRDI QIDQ1616100

Javier A. Almonacid, Ricardo Oyarzúa, Gabriel N. Gatica

Publication date: 31 October 2018

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-018-0278-z

zbMATH Keywords

fixed point theoryfinite element methodsBoussinesq equationsa priori error analysisaugmented mixed-primal formulation

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Forced convection (76R05) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (17)

Stabilized finite element approximations for a generalized Boussinesq problem: a posteriori error analysis ⋮ Analysis of a semi-augmented mixed finite element method for double-diffusive natural convection in porous media ⋮ A decoupled and iterative finite element method for generalized Boussinesq equations ⋮ A posteriori error analysis of a mixed-primal finite element method for the Boussinesq problem with temperature-dependent viscosity ⋮ Mixed-primal methods for natural convection driven phase change with Navier-Stokes-Brinkman equations ⋮ A new mixed finite element method for the \(n\)-dimensional Boussinesq problem with temperature-dependent viscosity ⋮ A divergence-conforming DG-mixed finite element method for the stationary Boussinesq problem ⋮ A Banach spaces-based analysis of a new fully-mixed finite element method for the Boussinesq problem ⋮ A fully-mixed finite element method for the \(n\)-dimensional Boussinesq problem with temperature-dependent parameters ⋮ A Banach spaces-based analysis of a new mixed-primal finite element method for a coupled flow-transport problem ⋮ Ultra-weak symmetry of stress for augmented mixed finite element formulations in continuum mechanics ⋮ Stability and finite element approximation of phase change models for natural convection in porous media ⋮ New mixed finite element methods for natural convection with phase-change in porous media ⋮ An analysis of weak Galerkin finite element method for a steady state Boussinesq problem ⋮ A fully-mixed finite element method for the steady state Oberbeck-Boussinesq system ⋮ Versatile mixed methods for non-isothermal incompressible flows ⋮ A fractional-step DG-FE method for the time-dependent generalized Boussinesq equations

Uses Software

• UMFPACK
• FreeFem++
• MUMPS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stabilized finite element methods for the Oberbeck-Boussinesq model
• Dual-mixed finite element methods for the stationary Boussinesq problem
• A projection-based stabilized finite element method for steady-state natural convection problem
• An augmented mixed finite element method for linear elasticity with non-homogeneous Dirichlet conditions
• Multifrontal parallel distributed symmetric and unsymmetric solvers
• An augmented fully-mixed finite element method for the stationary Boussinesq problem
• Error estimates of finite element methods for nonstationary thermal convection problems with temperature-dependent coefficients
• Analysis of a conforming finite element method for the Boussinesq problem with temperature-dependent parameters
• An Augmented Mixed Finite Element Method for the Navier--Stokes Equations with Variable Viscosity
• A mixed-primal finite element approximation of a sedimentation–consolidation system
• Analysis of an augmented mixed-primal formulation for the stationary Boussinesq problem
• A Simple Introduction to the Mixed Finite Element Method
• A posteriorierror analysis for a viscous flow-transport problem
• Analysis of an augmented mixed-FEM for the Navier-Stokes problem
• A steepest gradient method for optimum structural design
• An augmented mixed-primal finite element method for a coupled flow-transport problem
• Finite Element Methods for Navier-Stokes Equations
• Mixed and Hybrid Finite Element Methods
• Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions
• Couplage des équations de Navier-Stokes et de la chaleur : le modèle et son approximation par éléments finis
• New development in freefem++
• A mixed formulation of Boussinesq equations: Analysis of nonsingular solutions
• An augmented stress‐based mixed finite element method for the steady state Navier‐Stokes equations with nonlinear viscosity
• The steady Navier–Stokes/energy system with temperature‐dependent viscosity—Part 2: The discrete problem and numerical experiments
• Algorithm 832
• An exactly divergence-free finite element method for a generalized Boussinesq problem

This page was built for publication: A mixed-primal finite element method for the Boussinesq problem with temperature-dependent viscosity