Residual-based a posteriori error estimation for multipoint flux mixed finite element methods

Shaohong Du; Shuyu Sun; Xiaoping Xie

doi:10.1007/s00211-015-0770-1

Residual-based a posteriori error estimation for multipoint flux mixed finite element methods

Shaohong Du, Shuyu Sun, Xiaoping Xie

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

A novel residual-type a posteriori error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimensions. The derived a posteriori error estimator for the velocity and pressure error in L-norm consists of discretization and quadrature indicators, and is shown to be reliable and efficient. The main tools of analysis are a locally postprocessed approximation to the pressure solution of an auxiliary problem and a quadrature error estimate. Numerical experiments are presented to illustrate the competitive behavior of the estimator.

Original language	English (US)
Pages (from-to)	197-222
Number of pages	26
Journal	Numerische Mathematik
Volume	134
Issue number	1
DOIs	https://doi.org/10.1007/s00211-015-0770-1
State	Published - Oct 26 2015

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was supported by National Natural Science Foundation of China (11171239) and Major Research Plan of National Natural Science Foundation of China (91430105).

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10.1007/s00211-015-0770-1

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title = "Residual-based a posteriori error estimation for multipoint flux mixed finite element methods",

abstract = "A novel residual-type a posteriori error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimensions. The derived a posteriori error estimator for the velocity and pressure error in L-norm consists of discretization and quadrature indicators, and is shown to be reliable and efficient. The main tools of analysis are a locally postprocessed approximation to the pressure solution of an auxiliary problem and a quadrature error estimate. Numerical experiments are presented to illustrate the competitive behavior of the estimator.",

author = "Shaohong Du and Shuyu Sun and Xiaoping Xie",

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AU - Du, Shaohong

AU - Sun, Shuyu

AU - Xie, Xiaoping

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This work was supported by National Natural Science Foundation of China (11171239) and Major Research Plan of National Natural Science Foundation of China (91430105).

PY - 2015/10/26

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N2 - A novel residual-type a posteriori error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimensions. The derived a posteriori error estimator for the velocity and pressure error in L-norm consists of discretization and quadrature indicators, and is shown to be reliable and efficient. The main tools of analysis are a locally postprocessed approximation to the pressure solution of an auxiliary problem and a quadrature error estimate. Numerical experiments are presented to illustrate the competitive behavior of the estimator.

AB - A novel residual-type a posteriori error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimensions. The derived a posteriori error estimator for the velocity and pressure error in L-norm consists of discretization and quadrature indicators, and is shown to be reliable and efficient. The main tools of analysis are a locally postprocessed approximation to the pressure solution of an auxiliary problem and a quadrature error estimate. Numerical experiments are presented to illustrate the competitive behavior of the estimator.

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JO - Numerische Mathematik

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Residual-based a posteriori error estimation for multipoint flux mixed finite element methods

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