p-拉普拉斯问题的内罚不连续伽辽金近似的平衡后验误差估计

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-12-01 DOI:10.1515/rnam-2021-0026

R. Hoppe, Youri Iliash

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引用次数: 0

摘要

摘要我们讨论了p-Laplace方程的内部惩罚间断Galerkin（IPDG）近似和平衡后验误差估计。IPDG方法可以从涉及适当定义的重建算子的相关最小化问题的离散化中导出。平衡后验误差估计器为破碎的W1，p范数中的离散化误差提供了上界，并且依赖于根据与IPDG近似的混合公式相关联的数值通量函数来构造平衡通量。建立了残差型后验误差估计器与残差型的关系。数值结果说明了这两种估计的性能。

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An equilibrated a posteriori error estimator for an Interior Penalty Discontinuous Galerkin approximation of the p-Laplace problem

Abstract We are concerned with an Interior Penalty Discontinuous Galerkin (IPDG) approximation of the p-Laplace equation and an equilibrated a posteriori error estimator. The IPDG method can be derived from a discretization of the associated minimization problem involving appropriately defined reconstruction operators. The equilibrated a posteriori error estimator provides an upper bound for the discretization error in the broken W1,p norm and relies on the construction of an equilibrated flux in terms of a numerical flux function associated with the mixed formulation of the IPDG approximation. The relationship with a residual-type a posteriori error estimator is established as well. Numerical results illustrate the performance of both estimators.

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来源期刊

Russian Journal of Numerical Analysis and Mathematical Modelling 数学-工程：综合

CiteScore

1.40

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Russian Journal of Numerical Analysis and Mathematical Modelling, published bimonthly, provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling. The editorial board, consisting of the most prominent Russian scientists in numerical analysis and mathematical modelling, selects papers on the basis of their high scientific standard, innovative approach and topical interest. Topics: -numerical analysis- numerical linear algebra- finite element methods for PDEs- iterative methods- Monte-Carlo methods- mathematical modelling and numerical simulation in geophysical hydrodynamics, immunology and medicine, fluid mechanics and electrodynamics, geosciences.