A fractional-step DG-FE method for the time-dependent generalized Boussinesq equations

DOI10.1016/j.cnsns.2022.106884zbMath1500.65062OpenAlexW4295981439MaRDI QIDQ2094500

Yuanyuan Hou, Jiangyong Hou, Wen-Jing Yan

Publication date: 28 October 2022

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2022.106884

zbMATH Keywords

error analysisdiscontinuous Galerkin methodfractional-step methodtime-dependent generalized Boussinesq equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical analysis and computation of a type of IMEX method for the time-dependent natural convection problem
• A projection-based stabilized finite element method for steady-state natural convection problem
• A posteriori error estimation and adaptive computation of conduction convection problems
• An analysis of the fractional step method
• Boundary conditions for incompressible flows
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• High-order splitting methods for the incompressible Navier-Stokes equations
• A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• A new class of truly consistent splitting schemes for incompressible flows
• A mixed-primal finite element method for the Boussinesq problem with temperature-dependent viscosity
• Decoupled scheme for time-dependent natural convection problem. II: Time semidiscreteness
• Finite element methods for symmetric hyperbolic equations
• Stationary solutions for generalized Boussinesq models
• Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
• 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
• Stabilized finite element approximations for a generalized Boussinesq problem: a posteriori error analysis
• Numerical analysis of the unconditionally stable discontinuous Galerkin schemes for the nonstationary conduction-convection problem
• Decoupled two level finite element methods for the steady natural convection problem
• An efficient two-level finite element algorithm for the natural convection equations
• Estimation of penalty parameters for symmetric interior penalty Galerkin methods
• An overview of projection methods for incompressible flows
• The local discontinuous Galerkin method for linearized incompressible fluid flow: a review
• Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires. II
• 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 A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
• Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
• Quelques résultats nouveaux sur les méthodes de projection
• On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 2: Implementation
• Error analysis for finite element methods for steady natural convection problems
• A Banach spaces-based analysis of a new fully-mixed finite element method for the Boussinesq problem
• The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• A Second-Order Accurate Pressure-Correction Scheme for Viscous Incompressible Flow
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• The initial value problem for a generalized Boussinesq model
• A fractional-step method for the incompressible Navier-Stokes equations related to a predictor-multicorrector algorithm
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Velocity-Correction Projection Methods for Incompressible Flows
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• A locally conservative LDG method for the incompressible Navier-Stokes equations
• A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems
• A Coupled Prediction Scheme for Solving the Navier--Stokes and Convection-Diffusion Equations
• 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
• An exactly divergence-free finite element method for a generalized Boussinesq problem
• Numerical Solution of the Navier-Stokes Equations
• AN APPROXIMATE PROJECTION SCHEME FOR INCOMPRESSIBLE FLOW USING SPECTRAL ELEMENTS
• A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations

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