Selfadjoint Schrödinger operators on the half-space with compactly supported Robin boundary conditions

PAMM ◽  
2011 ◽  
Vol 11 (1) ◽  
pp. 885-886
Author(s):  
Jussi Behrndt ◽  
Christian Kühn ◽  
Jonathan Rohleder
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Robin Boundary Conditions ◽  
Compactly Supported ◽  
Robin Boundary

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.

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