scholarly journals Handling Neumann and Robin boundary conditions in a fictitious domain volume penalization framework

2022 ◽  
Vol 448 ◽  
pp. 110726
Author(s):  
Ramakrishnan Thirumalaisamy ◽  
Neelesh A. Patankar ◽  
Amneet Pal Singh Bhalla
Keyword(s):  
Boundary Conditions ◽  
Fictitious Domain ◽  
Robin Boundary Conditions ◽  
Robin Boundary

A Least-Squares/Fictitious Domain Method for Linear Elliptic Problems with Robin Boundary Conditions

2011 ◽  
Vol 9 (3) ◽  
pp. 587-606 ◽  
Author(s):  
Roland Glowinski ◽  
Qiaolin He
Keyword(s):  
Boundary Conditions ◽  
Least Squares ◽  
Gradient Algorithm ◽  
Fictitious Domain ◽  
Optimal Order ◽  
Robin Boundary Conditions ◽  
Fictitious Domain Method ◽  
Optimal Order Of Convergence ◽  
Domain Method ◽  
Robin Boundary

AbstractIn this article, we discuss a least-squares/fictitious domain method for the solution of linear elliptic boundary value problems with Robin boundary conditions. Let Ω and ω be two bounded domains of Rd such that ω̅⊂Ω. For a linear elliptic problem in Ω\ω̅ with Robin boundary condition on the boundary ϒ of ω, our goal here is to develop a fictitious domain method where one solves a variant of the original problem on the full Ω, followed by a well-chosen correction over ω. This method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. Numerical results obtained when applying our method to the solution of two-dimensional elliptic and parabolic problems are given; they suggest optimal order of convergence.

scholarly journals An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Li-Bin Liu ◽  
Ying Liang ◽  
Xiaobing Bao ◽  
Honglin Fang
Keyword(s):  
Boundary Conditions ◽  
Grid Method ◽  
Posteriori Error ◽  
Adaptive Grid ◽  
Singularly Perturbed ◽  
Robin Boundary Conditions ◽  
Euler Formula ◽  
Convection Diffusion ◽  
Backward Euler ◽  
Robin Boundary

AbstractA system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval $[0,1]$ [ 0 , 1 ] . It is shown that any solution of such a problem can be expressed to a system of first-order singularly perturbed initial value problem, which is discretized by the backward Euler formula on an arbitrary nonuniform mesh. An a posteriori error estimation in maximum norm is derived to design an adaptive grid generation algorithm. Besides, in order to establish the initial values of the original problems, we construct a nonlinear optimization problem, which is solved by the Nelder–Mead simplex method. Numerical results are given to demonstrate the performance of the presented method.

scholarly journals Logarithmic minimal models with Robin boundary conditions

2016 ◽  
Vol 2016 (6) ◽  
pp. 063104 ◽  
Author(s):  
Jean-Emile Bourgine ◽  
Paul A Pearce ◽  
Elena Tartaglia
Keyword(s):  
Boundary Conditions ◽  
Robin Boundary Conditions ◽  
Minimal Models ◽  
Robin Boundary
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