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A MODIFIED WEAK GALERKIN FINITE ELEMENTMETHOD FOR SINGULARLY PERTURBED parabolic convection-diffusion-REACTION problems

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Journal of Computational Mathematics 2023年第6期41卷 1246-1280页

作者： Suayip Toprakseven Fuzheng Gao Faculty of Engineering Department of Computer ScienceArtvin Coruh UniversityArtvin08100Turkey School of Mathematics Shandong UniversityJinan 250100China

In this work,a modified weak Galerkin finite element method is proposed for solving second order linear parabolic singularly perturbed convection-diffusion *** key feature of the proposed method is to replace the classical gradient and divergence operators by the modified weak gradient and modified divergence operators,*** apply the backward finite difference method in time and the modified weak Galerkin finite element method in space on uniform *** stability analyses are presented for both semi-discrete and fully-discrete modified weak Galerkin finite element *** order of convergences are obtained in suitable *** have achieved the same accuracy with the weak Galerkin method while the degrees of freedom are reduced in our *** numerical examples are presented to support the theoretical *** is theoretically and numerically shown that the method is quite stable.

关键词： The modified weak Galerkin finite element method Backward Euler method parabolic convection-diffusion problems Error estimates

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A parameter-uniform hybrid finite difference scheme for singularly perturbed system of parabolic convection-diffusion problems

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2020年第4期97卷 875-905页

作者： Singh, Maneesh Kumar Natesan, Srinivasan Indian Inst Technol Dept Math Gauhati India

We present the hybrid finite difference scheme for singularly perturbed system of parabolic convection-diffusion problems exhibiting overlapping boundary layers. We discretize the time derivative by the backward-Euler method and the spatial derivatives is discretized by the hybrid difference scheme on Shishkin mesh. We have shown that the presented numerical scheme is parameter-uniform convergent of first-order in temporal variable and almost second-order in spatial variable. Numerical experiments supporting the theoretical results are presented.

关键词： Singularly perturbed system parabolic convection-diffusion problems boundary layers piecewise-uniform Shishkin mesh hybrid finite difference scheme uniform convergence CR G1 8

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A method of line with improved accuracy for singularly perturbed parabolic convection-diffusion problems with large temporal lag

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RESULTS IN APPLIED MATHEMATICS 2021年 11卷

作者： Negero, Naol Tufa Duressa, Gemechis File Wollega Univ Dept Math Nekemte Ethiopia Jimma Univ Dept Math Jimma Ethiopia

A robust numerical scheme is proposed to solve singularly perturbed large time-delay parabolic convection-diffusion problems. For domain discretization, the backward-Euler method for the time derivative and Micken's type discretization for the space derivatives are used. Using a Richardson extrapolation technique the e-uniform accuracy of the method is improved to second order convergences. We present numerical examples to confirm the agreement of the numerical methods with the theoretical results. The proposed numerical scheme is parameter-uniform convergent, more accurate and robust. (C) 2021 The Author(s). Published by Elsevier B.V.

关键词： parabolic convection-diffusion problems Time delay Method of lines Uniform convergence

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A fitted operator finite difference method of lines for singularly perturbed parabolic convection-diffusion problems

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MATHEMATICS AND COMPUTERS IN SIMULATION 2019年 165卷 156-171页

作者： Mbroh, Nana A. Munyakazi, Justin B. Univ Western Cape Dept Math & Appl Math Private Bag X17 ZA-7535 Bellville South Africa

We propose a uniformly convergent finite difference method to solve singularly perturbed time-dependent convection- diffusion problems in the framework of method of lines. The method uses the fitted operator finite difference method to discretize the spatial derivatives followed by the Crank-Nicolson method for the time derivative. Richardson extrapolation is performed in space to improve the accuracy of the method. We prove that the method is uniformly convergent with respect to the perturbation and the discretization parameters. We present numerical simulations to illustrate and confirm the theoretical results. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： parabolic convection-diffusion problems Singular perturbations Fitted operator finite difference methods Convergence analysis Method of lines

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Uniform Convergent Solution of Singularly Perturbed parabolic Differential Equations with General Temporal-Lag

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IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE 2022年第2期46卷 507-524页

作者： Negero, Naol Tufa Duressa, Gemechis File Wollega Univ Dept Math Nekemte Ethiopia Jimma Univ Dept Math Jimma Ethiopia

In this paper, we presented a parameter uniform B-spline collocation nonstandard finite difference scheme for a class of singularly perturbed parabolic one-dimensional convection-diffusion problems with a time delay on a uniform mesh. When the delay parameter is smaller than the perturbation parameter, the delayed term is expanded in Taylor series and a B-spline collocation tridiagonal nonstandard finite difference scheme is developed. Here, the proposed finite difference scheme is unconditionally stable and is first-order convergent in the temporal direction and second-order accurate in the spatial direction. When the delay parameter is larger than the perturbation parameter, a special type of mesh is used for the temporal variable so that the delay lie on the nodal points and B-spline collocation nonstandard finite difference scheme is developed. The scheme is also unconditionally stable and is first-order convergent in the temporal direction and second-order accurate in the spatial direction. We carried out numerical simulations to verify the theoretical results.

关键词： Singular perturbation parabolic convection-diffusion problems Time delay B-spline collocation nonstandard finite difference method Boundary layer

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Numerical Analysis of Singularly Perturbed System of parabolic convection-diffusion Problem with Regular Boundary Layers

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DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS 2022年第3期30卷 695-717页

作者： Singh, Maneesh Kumar Natesan, Srinivasan Indian Inst Technol Guwahati Dept Math Gauhati 781039 India

In this article, we obtain the numerical solution of singularly perturbed system of parabolic convection-diffusion problems exhibiting boundary layer. The proposed numerical scheme consists of the backward-Euler method for the time derivative and an upwind finite difference scheme for the spatial derivatives. We analyze the scheme on a piecewise-uniform Shishkin mesh for the spatial discretization to establish uniform convergence with respect to the perturbation parameters. For the proposed scheme, the stability analysis is presented and parameter-uniform error estimate is derived. In order to validate the theoretical results, we have carried out some numerical experiments.

关键词： Singularly perturbed system parabolic convection-diffusion problems Boundary layers Shishkin mesh Finite difference scheme Uniform convergence

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