scholarly journals Strong Convergence of a Fully Discrete Finite Element Approximation of the Stochastic Cahn--Hilliard Equation

2018 ◽  
Vol 56 (2) ◽  
pp. 708-731 ◽  
Author(s):  
Daisuke Furihata ◽  
Mihály Kovács ◽  
Stig Larsson ◽  
Fredrik Lindgren
Keyword(s):  
Finite Element ◽  
Strong Convergence ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Fully Discrete ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation ◽  
Discrete Finite Element

scholarly journals Fully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-21
Author(s):  
Jae-Hong Pyo
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Boussinesq Equations ◽  
Finite Element Approximation ◽  
Navier Stokes ◽  
Element Approximation ◽  
Uzawa Method ◽  
Element Space ◽  
Fully Discrete ◽  
Discrete Finite Element

The stabilized Gauge-Uzawa method (SGUM), which is a 2nd-order projection type algorithm used to solve Navier-Stokes equations, has been newly constructed in the work of Pyo, 2013. In this paper, we apply the SGUM to the evolution Boussinesq equations, which model the thermal driven motion of incompressible fluids. We prove that SGUM is unconditionally stable, and we perform error estimations on the fully discrete finite element space via variational approach for the velocity, pressure, and temperature, the three physical unknowns. We conclude with numerical tests to check accuracy and physically relevant numerical simulations, the Bénard convection problem and the thermal driven cavity flow.

scholarly journals A fully discrete finite element scheme for the Kelvin-Voigt model

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5813-5827 ◽  
Author(s):  
Xiaoli Lu ◽  
Lei Zhang ◽  
Pengzhan Huang
Keyword(s):  
Finite Element ◽  
Time Discretization ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Step Method ◽  
Fully Discrete ◽  
Space Discretization ◽  
Voigt Model ◽  
Discrete Finite Element ◽  
Present Algorithm

In this paper, we study convergence of a fully discrete scheme for the two-dimensional nonstationary Kelvin-Voigt model. This scheme is based on a finite element approximation for space discretization and the Crank-Nicolson-type scheme for time discretization, which is a two step method. Moreover, we obtain error estimates of velocity and pressure. At last, the applicability and effectiveness of the present algorithm are illustrated by numerical experiments.

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