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首页> 外文期刊>Applications of Mathematics >RICHARDSON EXTRAPOLATION AND DEFECT CORRECTION OF MIXED FINITE ELEMENT METHODS FOR INTEGRO-DIFFERENTIAL EQUATIONS IN POROUS MEDIA
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RICHARDSON EXTRAPOLATION AND DEFECT CORRECTION OF MIXED FINITE ELEMENT METHODS FOR INTEGRO-DIFFERENTIAL EQUATIONS IN POROUS MEDIA

机译：多孔介质中积分微分方程的混合有限元方法的RICHARDSON外推和修正

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摘要

Asymptotic error expansions in the sense of L~∞-norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing technique, and the key point in deriving them is the establishment of the error estimates for the mixed regularized Green's functions with memory terms presented in R. Ewing at al., Int. J. Numer. Anal. Model 2 (2005), 301-328. As a result of all these higher order numerical approximations, they can be used to generate a posteriori error estimators for this mixed finite element approximation.
机译：通过与矩形域上一类抛物积分微分方程相关联的最低阶矩形元素，推导Raviart-Thomas混合有限元逼近的L〜∞范数渐近误差展开，从而进行Richardson外推两种不同方案的组合，并且可以通过插值后处理技术应用插值缺陷校正来提高矢量场和标量场的近似精度，而推导它们的关键是误差的建立R. Ewing等人（Int。）提出的带有记忆项的混合正则格林函数的估计。 J.纽默肛门模型2（2005），301-328。所有这些更高阶数值近似的结果是，它们可用于生成此混合有限元近似的后验误差估计量。

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