Finite Volume Superconvergence Approximation for One-Dimensional Singularly Perturbed Problems

2013 ◽  
Vol 31 (5) ◽  
pp. 488-508 ◽  
Author(s):  
Waixiang Cao
Keyword(s):  
Finite Volume ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems ◽  
One Dimensional

Численный анализ законов сгущения сеток для задач со степенными погранслоями первого типа

2020 ◽  
Author(s):  
V.D. Liseikin ◽  
S. Karasuljic
Keyword(s):  
Boundary Layers ◽  
Numerical Experiments ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems ◽  
One Dimensional ◽  
Type Boundary

This paper demonstrates results of numerical experiments on some popular and new layer-resolving grids applied for solving one-dimensional singularly-perturbed problems having power of the first type boundary layers. В статье приведены результаты численных расчетов обыкновенных сингулярно-возмущенных задач, решения которых имеют степенные, первого типа, пограничные слои. Расчеты проведены с использованием как известных адаптивных сеток, сгущающихся в слоях, так и новых. Численные эксперименты демонстрируют преимущество новых сеток.

Regularization of Integral Operators in Singularly Perturbed Problems Using Normal Forms

Vestnik MEI ◽  
2019 ◽  
Vol 6 ◽  
pp. 131-137
Author(s):  
Abdukhafiz A. Bobodzhanova ◽  
◽  
Valeriy F. Safonov ◽  
Keyword(s):  
Normal Forms ◽  
Integral Operators ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems

A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems

2017 ◽  
Vol 17 (2) ◽  
pp. 337-349 ◽  
Author(s):  
Christos Xenophontos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fourth Order ◽  
Hermite Polynomials ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
The Finite Element Method ◽  
Singularly Perturbed Problems ◽  
Exponentially Graded ◽  
Element Method

AbstractWe consider fourth order singularly perturbed problems in one-dimension and the approximation of their solution by the h version of the finite element method. In particular, we use piecewise Hermite polynomials of degree ${p\geq 3}$ defined on an exponentially graded mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at the optimal rate when the error is measured in both the energy norm and a stronger, ‘balanced’ norm. Finally, we illustrate our theoretical findings through numerical computations, including a comparison with another scheme from the literature.

Sign in / Sign up

Export Citation Format

Share Document