Year: 2024
Author: Li Feng, Zhongyi Huang
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 5 : pp. 1356–1379
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2305-m2022-0171
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 5 : pp. 1356–1379
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Turning point problem Petrov-Galerkin finite element method Uniform convergency.