TY - JOUR
T1 - The Singularity-Separated Method for the Singular Perturbation Problems in 1-D
AU - Chen , Chuanmiao
AU - Yang , Jing
JO - International Journal of Numerical Analysis and Modeling
VL - 1-2
SP - 102
EP - 110
PY - 2018
DA - 2018/01
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10558.html
KW - Singular perturbation problem, singularity-separated method, third boundary value, second order regularity, finite elements.
AB - <p style="text-align: justify;">The singularity-separated method (SSM) for the singular perturbation problem $-\epsilon u&#39;&#39;+bu&#39; + cu = f(x), u(0) = u(1) = 0$, is proposed for the first time. The solution is expressed as $u = w-ν$, where $w$ is the solution of corresponding third boundary value problem and $ν$ is an exact singular function. We have proved a global regularity, $||w||_2 ≤ C$, where the constant $C$ is independent of $\epsilon$, and discussed three kinds of finite element (FE) methods with SSM. Numerical results show that these FE-solutions have the high accuracy when only one element in boundary layer is taken.</p>