A new mixed finite element method for the \(n\)-dimensional Boussinesq problem with temperature-dependent viscosity

DOI10.3934/NHM.2020010zbMath1446.65155OpenAlexW3016006100MaRDI QIDQ2197225

Javier A. Almonacid, Ricardo Ruiz-Baier, Ricardo Oyarzúa, Gabriel N. Gatica

Publication date: 28 August 2020

Published in: Networks and Heterogeneous Media (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/nhm.2020010

zbMATH Keywords

finite element methodsBoussinesq equationsa priori error analysisfixed-point theoryaugmented mixed-primal formulation

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Forced convection (76R05) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Diffusive and convective heat and mass transfer, heat flow (80A19)

Related Items (5)

A dual-mixed approximation for a huber regularization of generalized \(p\)-Stokes viscoplastic flow problems ⋮ New non-augmented mixed finite element methods for the Navier-Stokes-Brinkman equations using Banach spaces ⋮ Mixed-primal methods for natural convection driven phase change with Navier-Stokes-Brinkman equations ⋮ Analysis of an augmented fully-mixed finite element method for a bioconvective flows model ⋮ Versatile mixed methods for non-isothermal incompressible flows

Uses Software

• MUMPS
• FEniCS

Cites Work

• 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
• Multifrontal parallel distributed symmetric and unsymmetric solvers
• A mixed-primal finite element method for the Boussinesq problem with temperature-dependent viscosity
• A full discretisation of the time-dependent Boussinesq (buoyancy) model with nonlinear viscosity
• A fully-mixed finite element method for the \(n\)-dimensional Boussinesq problem with temperature-dependent parameters
• A divergence-free low-order stabilized finite element method for a generalized steady state Boussinesq problem
• 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
• Mass-corrections for the conservative coupling of flow and transport on collocated meshes
• On the Navier-Stokes equations with temperature-dependent transport coefficients
• 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
• A refined mixed finite element method for the boussinesq equations in polygonal domains
• 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
• Analysis of fully-mixed finite element methods for the Stokes-Darcy coupled problem
• An augmented mixed-primal finite element method for a coupled flow-transport problem
• An analysis of the finite element method for natural convection problems
• Mixed and Hybrid Finite Element Methods
• Minimum-time isochronal surfaces for certain third-order systems
• Rapidly rotating turbulent Rayleigh-Bénard convection
• Error analysis of an augmented mixed method for the Navier–Stokes problem with mixed boundary conditions
• Couplage des équations de Navier-Stokes et de la chaleur : le modèle et son approximation par éléments finis
• A mixed formulation of Boussinesq equations: Analysis of nonsingular solutions
• Several iterative schemes for the stationary natural convection equations at different <scp>R</scp>ayleigh numbers
• 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 1: Analysis of the continuous problem
• The steady Navier–Stokes/energy system with temperature‐dependent viscosity—Part 2: The discrete problem and numerical experiments

This page was built for publication: A new mixed finite element method for the \(n\)-dimensional Boussinesq problem with temperature-dependent viscosity