TY - JOUR
T1 - A Uniform Convergent Petrov-Galerkin Method for a Class of Turning Point Problems
AU - Feng , Li
AU - Huang , Zhongyi
JO - Journal of Computational Mathematics
VL - 5
SP - 1356
EP - 1379
PY - 2024
DA - 2024/07
SN - 42
DO - http://doi.org/10.4208/jcm.2305-m2022-0171
UR - https://global-sci.org/intro/article_detail/jcm/23281.html
KW - Turning point problem, Petrov-Galerkin finite element method, Uniform convergency.
AB - <p style="text-align: justify;">In this paper, we propose a numerical method for turning point problems in one dimension based on Petrov-Galerkin finite element method (PGFEM). We first give a priori
estimate for the turning point problem with a single boundary turning point. Then we use
PGFEM to solve it, where test functions are the solutions to piecewise approximate dual
problems. We prove that our method has a first-order convergence rate in both $L^∞_h$ norm
and a discrete energy norm when we select the exact solutions to dual problems as test
functions. Numerical results show that our scheme is efficient for turning point problems
with different types of singularities, and the convergency coincides with our theoretical
results.</p>