Regularity of an elliptic problem with mixed Dirichlet-Robin boundary conditions in a polygonal domain

CALCOLO ◽  
1992 ◽  
Vol 29 (3-4) ◽  
pp. 241-267 ◽  
Author(s):  
Z. Mghazli
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problem ◽  
Robin Boundary Conditions ◽  
Polygonal Domain ◽  
Robin Boundary

scholarly journals The Brezis–Oswald Result for Quasilinear Robin Problems

2016 ◽  
Vol 16 (3) ◽  
Author(s):  
Genni Fragnelli ◽  
Dimitri Mugnai ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Elliptic Problem ◽  
Robin Boundary Conditions ◽  
Nonlinear Elliptic Problem ◽  
Reaction Term ◽  
Nonhomogeneous Differential Operator ◽  
Nonlinear Elliptic ◽  
Robin Boundary

AbstractIn this paper we consider a nonlinear elliptic problem driven by a nonhomogeneous differential operator with Robin boundary conditions. We produce conditions on the reaction term near

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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