scholarly journals A new discontinuous Galerkin method for the nonlinear Poisson–Boltzmann equation

2015 ◽  
Vol 49 ◽  
pp. 126-132 ◽  
Author(s):  
Weishan Deng ◽  
Xiaohe Zhufu ◽  
Jin Xu ◽  
Shan Zhao
Keyword(s):  
Boltzmann Equation ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

An Iterative Discontinuous Galerkin Method for Solving the Nonlinear Poisson Boltzmann Equation

2014 ◽  
Vol 16 (2) ◽  
pp. 491-515 ◽  
Author(s):  
Peimeng Yin ◽  
Yunqing Huang ◽  
Hailiang Liu
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Solution Space ◽  
Initial Guess ◽  
Two Dimensional ◽  
Order Of Accuracy ◽  
Dg Method ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

AbstractAn iterative discontinuous Galerkin (DG) method is proposed to solve the nonlinear Poisson Boltzmann (PB) equation. We first identify a function space in which the solution of the nonlinear PB equation is iteratively approximated through a series of linear PB equations, while an appropriate initial guess and a suitable iterative parameter are selected so that the solutions of linear PB equations are monotone within the identified solution space. For the spatial discretization we apply the direct discontinuous Galerkin method to those linear PB equations. More precisely, we use one initial guess when the Debye parameterλ=(1), and a special initial guess forλ≫1 to ensure convergence. The iterative parameter is carefully chosen to guarantee the existence, uniqueness, and convergence of the iteration. In particular, iteration steps can be reduced for a variable iterative parameter. Both one and two-dimensional numerical results are carried out to demonstrate both accuracy and capacity of the iterative DG method for both cases ofλ=(1) andλ≪ 1. The (m+ 1)th order of accuracy forL2andmth order of accuracy forH1forPmelements are numerically obtained.

SELECTION OF VISCOUS TERMS APPROXIMATION IN DISCONTINUOUS GALERKIN METHOD

2013 ◽  
Vol 44 (3) ◽  
pp. 327-354
Author(s):  
Aleksey Igorevich Troshin ◽  
Vladimir Viktorovich Vlasenko ◽  
Andrey Viktorovich Wolkov
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Selection Of
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