A posteriori error estimates of finite element methods by preconditioning

Yuwen Li; Ludmil Zikatanov

doi:10.1016/j.camwa.2020.08.001

A posteriori error estimates of finite element methods by preconditioning

Yuwen Li, Ludmil Zikatanov

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

2 Scopus citations

Abstract

We present a framework that relates preconditioning with a posteriori error estimates in finite element methods. In particular, we use standard tools in subspace correction methods to obtain reliable and efficient error estimators. As a simple example, we recover the classical residual error estimators for the second order elliptic equations.

Original language	English (US)
Pages (from-to)	192-201
Number of pages	10
Journal	Computers and Mathematics with Applications
Volume	91
DOIs	https://doi.org/10.1016/j.camwa.2020.08.001
State	Published - Jun 1 2021

All Science Journal Classification (ASJC) codes

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2020.08.001

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title = "A posteriori error estimates of finite element methods by preconditioning",

abstract = "We present a framework that relates preconditioning with a posteriori error estimates in finite element methods. In particular, we use standard tools in subspace correction methods to obtain reliable and efficient error estimators. As a simple example, we recover the classical residual error estimators for the second order elliptic equations.",

author = "Yuwen Li and Ludmil Zikatanov",

note = "Funding Information: The work of Zikatanov was supported in part by NSF, United States of America grants DMS-1720114 and DMS-1819157 . Publisher Copyright: {\textcopyright} 2020 Elsevier Ltd",

year = "2021",

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doi = "10.1016/j.camwa.2020.08.001",

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AU - Zikatanov, Ludmil

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AB - We present a framework that relates preconditioning with a posteriori error estimates in finite element methods. In particular, we use standard tools in subspace correction methods to obtain reliable and efficient error estimators. As a simple example, we recover the classical residual error estimators for the second order elliptic equations.

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JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

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A posteriori error estimates of finite element methods by preconditioning

Abstract

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