DISCONTINUOUS DISCRETIZATION FOR LEAST-SQUARES FORMULATION OF SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS IN ONE AND TWO DIMENSIONS

RUNCHANG LIN

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DISCONTINUOUS DISCRETIZATION FOR LEAST-SQUARES FORMULATION OF SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS IN ONE AND TWO DIMENSIONS

机译：一维和二维奇摄动反应扩散问题的最小二乘解的不连续离散

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In this paper, we consider the singularly perturbed reaction-diffusion problem in one and two dimensions. The boundary value problem is decomposed into a first-order system to which a suitable weighted least-squares formulation is proposed. A robust, stable, and efficient approach is developed based on local discontinuous Galerkin (LDG) discretization for the weak form. Uniform error estimates are derived. Numerical examples are presented to illustrate the method and the theoretical results. Comparison studies are made between the proposed method and other methods.

机译：在本文中，我们考虑一维和二维奇摄动反应扩散问题。将边值问题分解为一阶系统，并针对该系统提出了合适的加权最小二乘公式。基于弱形式的局部不连续Galerkin（LDG）离散化，开发了一种鲁棒，稳定且高效的方法。得出均匀误差估计。数值例子说明了该方法和理论结果。所提出的方法与其他方法进行了比较研究。

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来源
《SIAM Journal on Numerical Analysis》 |2010年第1期|共20页
作者
RUNCHANG LIN;
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正文语种 eng
中图分类数值分析;
关键词
least-squares methods; local discontinuous Galerkin methods; singular perturbation problems; reaction-diffusion problems;

机译：最小二乘法;局部不连续伽勒金方法;奇摄动问题;反应扩散问题;

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专利

1. DISCONTINUOUS DISCRETIZATION FOR LEAST-SQUARES FORMULATION OF SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS IN ONE AND TWO DIMENSIONS [J] . RUNCHANG LIN SIAM Journal on Numerical Analysis . 2010,第1期

机译：一维和二维奇摄动反应扩散问题的最小二乘解的不连续离散
2. Discontinuous Galerkin least-squares finite element methods for singularly perturbed reaction-diffusion problems with discontinuous coefficients and boundary singularities [J] . Runchang Lin Numerische Mathematik . 2009,第2期

机译：具有不连续系数和边界奇异点的奇摄动反应扩散问题的不连续Galerkin最小二乘有限元方法
3. A discontinuous Galerkin least-squares finite element method for solving coupled singularly perturbed reaction-diffusion equations [J] . Lin Runchang Journal of Computational and Applied Mathematics . 2016,第Null期

机译：求解奇异摄动反应扩散方程的不连续Galerkin最小二乘有限元方法
4. The Error Analysis of Finite Difference Approximation for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations with Discontinuous Source Term [C] . S. Chandra Sekhara Rao, Sheetal Chawla International Conference on Finite Difference Methods . 2019

机译：具有不连续源术语单个扰动半线性反应扩散方程系统的有限差分近似的误差分析
5. Discontinuous Galerkin methods for singularly perturbed problems. [D] . Zhu, Huiqing. 2009

机译：奇异摄动问题的间断Galerkin方法。
6. Asymptotic Bounds for the Time-Periodic Solutions to the Singularly Perturbed Ordinary Differential Equations [O] . Gabil M. Amiraliyev, Aysenur Ucar 2013

机译：奇摄动常微分方程时间周期解的渐近界
7. Uniform convergence of discontinuous finite element methods for singularly perturbed reaction-diffusion problems [O] . Li Jichun 2002

机译：奇摄动反应扩散问题的不连续有限元方法的一致收敛
8. Least-squares streamline diffusion finite element approximations to singularly211 perturbed convection-diffusion problems [R] . Lazarov, R. D., Vassilevski, P. S. 1999

机译：最小二乘流线扩散有限元近似于奇异的211扰动对流 - 扩散问题

DISCONTINUOUS DISCRETIZATION FOR LEAST-SQUARES FORMULATION OF SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS IN ONE AND TWO DIMENSIONS

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