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Higher Order Uniformly Convergent Numerical Scheme for Singularly Perturbed Reaction-Diffusion Problems

Gemechis File Duressa|Worku Tilahun Anilay|Mesfi n Mekuria Woldaregay
경북대학교 자연과학대학 수학과|2021.09|Kyungpook Mathematical Journal|제61권 제3호|pp. 591-612

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참고문헌

키워드

Finite ElementFitted MeshParameter UniformSingularly Perturbed
주제분류수학

초록

In this paper, a uniformly convergent numerical scheme is designed for solving singularly perturbed reaction-difiusion problems. The problem is converted to an equivalent weak form and then a Galerkin finite element method is used on a piecewise uniform Shishkin mesh with linear basis functions. The convergence of the developed scheme is proved and it is shown to be almost fourth order uniformly convergent in the maximum norm. To exhibit the applicability of the scheme, model examples are considered and solved for di erent values of a singular perturbation parameter ε and mesh elements. The proposed scheme approximates the exact solution very well.

Abstract

In this paper, a uniformly convergent numerical scheme is designed for solving singularly perturbed reaction-difiusion problems. The problem is converted to an equivalent weak form and then a Galerkin finite element method is used on a piecewise uniform Shishkin mesh with linear basis functions. The convergence of the developed scheme is proved and it is shown to be almost fourth order uniformly convergent in the maximum norm. To exhibit the applicability of the scheme, model examples are considered and solved for di erent values of a singular perturbation parameter ε and mesh elements. The proposed scheme approximates the exact solution very well.

참고문헌 (23)

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