Numerical analysis of fully discrete energy stable weak Galerkin finite element Scheme for a coupled Cahn-Hilliard-Navier-Stokes phase-field model

2021 ◽  
Vol 410 ◽  
pp. 126487
Author(s):  
Mehdi Dehghan ◽  
Zeinab Gharibi
Keyword(s):  
Field Model ◽  
Phase Field Model ◽  
Navier Stokes ◽  
Weak Galerkin ◽  
Finite Element Scheme ◽  
Discrete Energy ◽  
Galerkin Finite Element ◽  
Element Scheme ◽  
Fully Discrete ◽  
Energy Stable

scholarly journals Energy Stable Discontinuous Galerkin Finite Element Method for the Allen–Cahn Equation

2018 ◽  
Vol 15 (03) ◽  
pp. 1850013 ◽  
Author(s):  
Bülent Karasözen ◽  
Murat Uzunca ◽  
Ayşe Sariaydin-Fi̇li̇beli̇oğlu ◽  
Hamdullah Yücel
Keyword(s):  
Galerkin Finite Element Method ◽  
Discrete Energy ◽  
Galerkin Finite Element ◽  
Energy Functionals ◽  
Fully Discrete ◽  
Cahn Equation ◽  
Degenerate Mobility ◽  
Discontinuous Galerkin Finite Element ◽  
Energy Stable ◽  
Logarithmic Energy

In this paper, we investigate numerical solution of Allen–Cahn equation with constant and degenerate mobility, and with polynomial and logarithmic energy functionals. We discretize the model equation by symmetric interior penalty Galerkin (SIPG) method in space, and by average vector field (AVF) method in time. We show that the energy stable AVF method as the time integrator for gradient systems like the Allen–Cahn equation satisfies the energy decreasing property for fully discrete scheme. Numerical results reveal that the discrete energy decreases monotonically, the phase separation and metastability phenomena can be observed, and the ripening time is detected correctly.

scholarly journals A weak Galerkin finite element scheme for the Cahn-Hilliard equation

2018 ◽  
Vol 88 (315) ◽  
pp. 211-235 ◽  
Author(s):  
Junping Wang ◽  
Qilong Zhai ◽  
Ran Zhang ◽  
Shangyou Zhang
Keyword(s):  
Finite Element ◽  
Weak Galerkin ◽  
Finite Element Scheme ◽  
Galerkin Finite Element ◽  
Element Scheme ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation
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