A Nonconforming Finite-Element Method for the Two-Dimensional Cahn–Hilliard Equation

1989 ◽  
Vol 26 (4) ◽  
pp. 884-903 ◽  
Author(s):  
Charles M. Elliott ◽  
Donald A. French
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nonconforming Finite Element ◽  
Two Dimensional ◽  
Nonconforming Finite Element Method ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation ◽  
Element Method

scholarly journals Nonconforming Finite Element Method Applied to the Driven Cavity Problem

2017 ◽  
Vol 21 (4) ◽  
pp. 1012-1038 ◽  
Author(s):  
Roktaek Lim ◽  
Dongwoo Sheen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Nonconforming Finite Element ◽  
Element Space ◽  
Nonconforming Finite Element Method ◽  
Driven Cavity ◽  
Dirichlet Data ◽  
Minimal Modification ◽  
Element Method

AbstractA cheapest stable nonconforming finite element method is presented for solving the incompressible flow in a square cavity without smoothing the corner singularities. The stable cheapest nonconforming finite element pair based on P1×P0 on rectangularmeshes [29] is employed with a minimal modification of the discontinuous Dirichlet data on the top boundary, where is the finite element space of piecewise constant pressures with the globally one-dimensional checker-board pattern subspace eliminated. The proposed Stokes elements have the least number of degrees of freedom compared to those of known stable Stokes elements. Three accuracy indications for our elements are analyzed and numerically verified. Also, various numerous computational results obtained by using our proposed element show excellent accuracy.

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