Finite element method for a nonlinear parabolic integro-differential equation in higher spatial dimensions

Nisha Sharma; Kapil K. Sharma

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Finite element method for a nonlinear parabolic integro-differential equation in higher spatial dimensions

机译：高空间尺度非线性抛物积分微分方程的有限元方法

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摘要

In this paper, we extend and analyze the Galerkin finite element method for the spatial discretization (Jangveladze et al., 2011) to the higher spatial dimensions and develop a numerical algorithm based on θ scheme for the time discretization for solving a parabolic integro-differential equation which arises in the magnetic field penetration process. A-pri-ori bounds are derived for the exact solution. The semi discrete and fully discrete error estimates are derived in L~∞(L~2(Ω)) and L~2(H~1(Ω)) norms using energy arguments. Further, we present a numerical experiment which supports the theoretical results.

机译：在本文中，我们将用于空间离散化的Galerkin有限元方法（Jangveladze等，2011）扩展和分析到更高的空间维，并开发了基于θ方案的时间离散化数值算法，以解决抛物线积分微分问题。在磁场穿透过程中出现的方程。得出精确解的先验界限。使用能量自变量在L〜∞（L〜2（Ω））和L〜2（H〜1（Ω））范数中得出半离散和完全离散的误差估计。此外，我们提出了一个支持理论结果的数值实验。

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来源
《Applied Mathematical Modelling》 |2015年第24期|7338-7350|共13页
作者
Nisha Sharma; Kapil K. Sharma;
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作者单位

Department of Mathematics, Panjab University, Chandigarh 160014, India;

Department of Mathematics, South Asian University, New Delhi, India;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Nonlinear integro-differential equations; Galerkin finite element method; Theta method; Projection;

机译：非线性积分微分方程;Galerkin有限元方法;Theta方法投影;

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1. H~1-Galerkin expanded mixed finite element methods for nonlinear pseudo-parabolic integro-differential equations [J] . Che H., Zhou Z., Jiang Z., Numerical Methods for Partial Differential Equations: An International Journal . 2013,第3期

机译：非线性伪抛物积分微分方程的H〜1-Galerkin扩展混合有限元方法
2. Finite element methods for partial Volterra integro-differential equations on two-dimensional unbounded spatial domains [J] . Ma JT Applied mathematics and computation . 2007,第1期

机译：二维无界空间域上Volterra积分微分方程的有限元方法
3. A two-grid finite element method for nonlinear parabolic integro-differential equations [J] . International journal of computer mathematics . 2019,第9a12期

机译：非线性抛物线积分微分方程的两网格有限元方法
4. Biquadric finite element method for parabolic integro-differential equations [C] . Liao Jingyu, Wang Fenling, Zhao Yanmin 2011 International Conference on Multimedia Technology . 2011

机译：抛物线积分微分方程的二元有限元方法
5. Decoupled Finite Element Methods for General Steady Two-Dimensional Boussinesq Equations [D] . ?Boveleth, Lioba 2020

机译：解耦有限元方法一般稳定二维 Boussinesq方程
6. A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things [O] . Rohul Amin, Shah Nazir, Iván García-Magariño 2020

机译：无线传感器网络与物联网非线性时滞积分微分方程数值解的配置方法
7. The stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equations of parabolic type [O] . Yanping Lin, Tie Zhang 1991

机译：RITZ-Volterra投影的稳定性与抛物面类型一类积分微分方程的有限元方法的稳定性
8. A Finite Element Method and Corresponding Pilot Computer Code for Hyperbolic Systems of Equations in Two Spatial Dimensions and Time Applied to Unsteady Gas Flows. [R] . schmitt,james a. 1977

机译：双曲线时空双曲方程组的有限元方法及相应的导频计算机编码应用于非定常气流。

Finite element method for a nonlinear parabolic integro-differential equation in higher spatial dimensions

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