A POSTERIORI ERROR ESTIMATION FOR THE DISCRETE DUALITY FINITE VOLUME DISCRETIZATION OF THE LAPLACE EQUATION

Omnes P; Penel Y; Rosenbaum Y

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A POSTERIORI ERROR ESTIMATION FOR THE DISCRETE DUALITY FINITE VOLUME DISCRETIZATION OF THE LAPLACE EQUATION

机译：Laplace方程离散对偶有限体积离散的Posteriori误差估计

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摘要

An efficient and fully computable a posteriori error bound is derived for the discrete duality finite volume discretization of the Laplace equation on very general two-dimensional meshes. The main ingredients are the equivalence of this method with a finite element like scheme and tools from the finite element framework. Numerical tests are performed with a stiff solution on highly nonconforming locally refined meshes and with a singular solution on triangular meshes.

机译：对于非常普通的二维网格上的Laplace方程的离散对偶有限体积离散，推导了一种有效且可完全计算的后验误差界。主要成分是这种方法与有限元（如方案和有限元框架中的工具）的等效性。在高度不合格的局部细化网格上使用刚性解进行数值测试，而在三角形网格上使用奇异解进行数值测试。

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《SIAM Journal on Numerical Analysis》 |2010年第4期|共26页
作者
Omnes P; Penel Y; Rosenbaum Y;
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正文语种 eng
中图分类数值分析;
关键词
a posteriori error estimation; finite volume; discrete duality; nonconforming meshes;

机译：后验误差估计;有限体积;离散对偶性;不合格网格;

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专利

1. A POSTERIORI ERROR ESTIMATION FOR THE DISCRETE DUALITY FINITE VOLUME DISCRETIZATION OF THE LAPLACE EQUATION [J] . Omnes P, Penel Y, Rosenbaum Y SIAM Journal on Numerical Analysis . 2010,第4期

机译：Laplace方程离散对偶有限体积离散的Posteriori误差估计
2. A posteriori error estimates for combined finite volume-finite element discretizations of reactive transport equations on nonmatching grids [J] . Danielle Hilhorst, Martin Vohralik Computer Methods in Applied Mechanics and Engineering . 2011,第5a8期

机译：非匹配网格上反应输运方程的有限体积-有限元离散化的后验误差估计
3. A posteriori error estimates for finite volume and mixed finite element discretizations of convection–diffusion–reaction equations [J] . Martin Vohralík ESAIM: Proceedings . 2007,第125期

机译：对流-扩散-反应方程的有限体积和混合有限元离散化的后验误差估计
4. Accuracy of Discretization Error Estimation by the Error Transport Equation on Unstructured Meshes - Nonlinear Systems of Equations [C] . Gary Kai Kin Yan, Carl Ollivier-Gooch AIAA computational fluid dynamics conference;AIAA aviation forum . 2015

机译：非结构网格上误差传递方程离散化误差估计的精度-非线性方程组
5. Estimation of grid-induced errors in computational fluid dynamics solutions using a discrete error transport equation. [D] . Williams, Brandon Riley. 2009

机译：使用离散误差传输方程估算计算流体动力学解决方案中的网格引起的误差。
6. A Posteriori Error Estimates for Fully Discrete Finite Element Method for Generalized Diffusion Equation with Delay [O] . Wansheng Wang, Lijun Yi, Aiguo Xiao -1

机译：时滞广义扩散方程全离散有限元法的后验误差估计。
7. A posteriori error estimation for the discrete duality finite volume discretization of the Laplace equation [O] . Omnes, Pascal, Penel, Yohan, Rosenbaum, Yann 2009

机译：拉普拉斯方程离散对偶有限体积离散化的后验误差估计

A POSTERIORI ERROR ESTIMATION FOR THE DISCRETE DUALITY FINITE VOLUME DISCRETIZATION OF THE LAPLACE EQUATION

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