Discrete Spline Solution of Singularly Perturbed Problem with Two Small Parameters on a Shishkin-Type Mesh

2018 ◽  
Vol 29 (3) ◽  
pp. 367-381 ◽  
Author(s):  
W. K. Zahra ◽  
M. Van Daele
Keyword(s):  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Small Parameters

Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters

2015 ◽  
Vol 7 (2) ◽  
pp. 196-206
Author(s):  
Yanping Chen ◽  
Haitao Leng ◽  
Li-Bin Liu
Keyword(s):  
Error Bound ◽  
A Priori ◽  
Diffusion Problem ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Optimal Error ◽  
Convection Diffusion ◽  
Small Parameters ◽  
Perturbation Parameters ◽  
Optimal Error Bound

AbstractIn this paper, we consider a singularly perturbed convection-diffusion problem. The problem involves two small parameters that gives rise to two boundary layers at two endpoints of the domain. For this problem, a non-monotone finite element methods is used. A priori error bound in the maximum norm is obtained. Based on the a priori error bound, we show that there exists Bakhvalov-type mesh that gives optimal error bound of (N−2) which is robust with respect to the two perturbation parameters. Numerical results are given that confirm the theoretical result.

scholarly journals Existence and Concentration Behavior of Solutions of the Critical Schrödinger–Poisson Equation in R3

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 464
Author(s):  
Jichao Wang ◽  
Ting Yu
Keyword(s):  
Poisson Equation ◽  
Existence Result ◽  
Critical Growth ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Number Of Solutions ◽  
Concentration Behavior ◽  
The Relationship ◽  
Concentration Phenomenon

In this paper, we study the singularly perturbed problem for the Schrödinger–Poisson equation with critical growth. When the perturbed coefficient is small, we establish the relationship between the number of solutions and the profiles of the coefficients. Furthermore, without any restriction on the perturbed coefficient, we obtain a different concentration phenomenon. Besides, we obtain an existence result.

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