Parallel two-grid finite element method for the time-dependent natural convection problem with non-smooth initial data

2019 ◽  
Vol 77 (8) ◽  
pp. 2221-2241
Author(s):  
Hongxia Liang ◽  
Tong Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Initial Data ◽  
Time Dependent ◽  
Smooth Initial Data ◽  
Convection Problem ◽  
Natural Convection Problem ◽  
Element Method

scholarly journals A Two-Grid Finite Element Method for Time-Dependent Incompressible Navier-Stokes Equations with Non-Smooth Initial Data

2015 ◽  
Vol 8 (4) ◽  
pp. 549-581 ◽  
Author(s):  
Deepjyoti Goswami ◽  
Pedro D. Damázio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Initial Data ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Smooth Initial Data ◽  
Element Method

AbstractWe analyze here, a two-grid finite element method for the two dimensional time-dependent incompressible Navier-Stokes equations with non-smooth initial data. It involves solving the non-linear Navier-Stokes problem on a coarse grid of size H and solving a Stokes problem on a fine grid of size h, h « H. This method gives optimal convergence for velocity in H1-norm and for pressure in L2-norm. The analysis mainly focuses on the loss of regularity of the solution at t = 0 of the Navier-Stokes equations.

Recovery-based error estimator for the natural-convection problem based on penalized finite element method

2019 ◽  
Vol 29 (12) ◽  
pp. 4850-4874
Author(s):  
Lulu Li ◽  
Haiyan Su ◽  
Jianping Zhao ◽  
Xinlong Feng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Posteriori Error ◽  
Optimal Error Estimates ◽  
Error Estimator ◽  
Content Type ◽  
Convection Problem ◽  
Natural Convection Problem ◽  
Element Method

Purpose This paper aims to proposes and analyzes a novel recovery-based posteriori error estimator for the stationary natural-convection problem based on penalized finite element method. Design/methodology/approach The optimal error estimates of the penalty FEM are established by using the lower-order finite element pair P1-P0-P1 which does not satisfy the discrete inf-sup condition. Besides, a new recovery type posteriori estimator in view of the gradient recovery and superconvergent theory to deal with the discontinuity of the gradient of numerical solution. Findings The stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations. Originality/value The provided reliability and efficiency analysis is shown that the true error can be effectively bounded by the recovery-based error estimator.

scholarly journals The Crank-Nicolson Extrapolation Stabilized Finite Element Method for Natural Convection Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-22
Author(s):  
Yunzhang Zhang ◽  
Yanren Hou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Time Level ◽  
Stabilized Finite Element ◽  
Fully Discrete ◽  
Stabilized Finite Element Method ◽  
Convection Problem ◽  
Natural Convection Problem ◽  
Element Method

This paper studies a fully discrete Crank-Nicolson linear extrapolation stabilized finite element method for the natural convection problem, which is unconditionally stable and has second order temporal accuracy ofO(Δt2+hΔt+hm). A simple artificial viscosity stabilized of the linear system for the approximation of the new time level connected to antidiffusion of its effects at the old time level is used. An unconditionally stability and an a priori error estimate are derived for the fully discrete scheme. A series of numerical results are presented that validate our theoretical findings.

An efficient iterative algorithm for the natural convection equations based on finite element method

2018 ◽  
Vol 28 (3) ◽  
pp. 584-605 ◽  
Author(s):  
Lei Wang ◽  
Jian Li ◽  
Pengzhan Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Iterative Method ◽  
Error Correction ◽  
Computational Time ◽  
Content Type ◽  
Natural Convection Problem ◽  
New Iterative Method ◽  
Element Method

Purpose This paper aims to propose a new highly efficient iterative method based on classical Oseen iteration for the natural convection equations. Design/methodology/approach First, the authors solve the problem by the Oseen iterative scheme based on finite element method, then use the error correction strategy to control the error arising. Findings The new iterative method not only retains the advantage of the Oseen scheme but also saves computational time and iterative step for solving the considered problem. Originality/value In this work, the authors introduce a new iterative method to solve the natural convection equations. The new algorithm consists of the Oseen scheme and the error correction which can control the errors from the iterative step arising for solving the nonlinear problem. Comparing with the classical iterative method, the new scheme requires less iterations and is also capable of solving the natural convection problem at higher Rayleigh number.

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