WEAK GALERKIN MIXED FINITE ELEMENT METHODS FOR PARABOLIC EQUATIONS WITH MEMORY

XIAOMENG LI; QIANG XU; AILING ZHU

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WEAK GALERKIN MIXED FINITE ELEMENT METHODS FOR PARABOLIC EQUATIONS WITH MEMORY

机译：具有记忆抛物型方程的弱Galerkin混合有限元方法

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We develop a semidiscrete and a backward Euler fully discrete weak Galerkin mixed finite element method for a parabolic differential equa-tion with memory. The optimal order error estimates in both｜ ‖ · ‖｜ and L~2 norms are established based on a generalized elliptic projection. In the numer-ical experiments, the equation is solved by the weak Galerkin schemes with spaces {[P_k(T)]~2; P_k(e),P_(k+1)(T)} for k = 0 and the numerical convergence rates confirm the theoretical results.

机译：我们开发了一个半色晶状态和落后的欧拉完全离散弱Galerkin混合有限元方法，用于记忆抛物型差动方程。基于广义的椭圆投影建立了‖·‖|和L〜2规范中的最佳顺序误差估计。在数值实验中，通过具有空间的弱Galerkin方案来解决方程{[p_k（t）]〜2; P_K（e），用于k = 0的P_（k + 1）（t）}，数值趋同率确认了理论结果。

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来源
《Discrete and continuous dynamical systems▼hSeries S》 |2019年第3期|513-531|共19页
作者
XIAOMENG LI; QIANG XU; AILING ZHU;
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作者单位

School of Mathematical and Statistics Shandong Normal University Jinan 250014 China;

School of Mathematical and Statistics Shandong Normal University Jinan 250014 China;

School of Mathematical and Statistics Shandong Normal University Jinan 250014 China;

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正文语种 eng
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关键词
Weak Galerkin; mixed finite element; discrete weak divergence; integro-differential equations; error estimates;

机译：弱galerkin;混合有限元;离散的弱分歧;积分微分方程;错误估计;

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2. Error estimates in weak Galerkin finite element methods for parabolic equations under low regularity assumptions [J] . Bhupen Deka, Naresh Kumar Applied numerical mathematics . 2021,第Apra期

机译：低规律假设下抛物方程弱Galerkin有限元方法的误差估计
3. Weak Galerkin finite element methods for linear parabolic integro-differential equations [J] . Zhu Ailing, Xu Tingting, Xu Qiang Numerical Methods for Partial Differential Equations: An International Journal . 2016,第5期

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4. H~1 -Galerkin expanded mixed finite element methods for pseudo-hyperbolicequations [C] . Meixia Li International Conference on Computational Materials Science . 2011

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5. Weak Galerkin Finite Element Methods for the Darcy Equation [D] . Wang, Zhuoran. 2018

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6. Numerical Analysis of an H1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation [O] . Jinfeng Wang, Meng Zhao, Min Zhang, -1

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7. Weak Galerkin mixed finite element methods for parabolic equations with memory [O] . Xiaomeng Li, Qiang Xu, Ailing Zhu 2019

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8. Solving a Parabolic Equation by the Combined Discontinuous-Galerkin Petrov-Galerkin Finite Element Method [R] . Freund, J. 1990

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WEAK GALERKIN MIXED FINITE ELEMENT METHODS FOR PARABOLIC EQUATIONS WITH MEMORY

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