A Posteriori Estimates Using Auxiliary Subspace Techniques

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A Posteriori Estimates Using Auxiliary Subspace Techniques. / Hakula, Harri; Neilan, Michael; Ovall, Jeffrey S.

In: JOURNAL OF SCIENTIFIC COMPUTING, Vol. 72, No. 1, 01.07.2017, p. 97-127.

Research output: Scientific - peer-reviewArticle

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Hakula, Harri; Neilan, Michael; Ovall, Jeffrey S. / A Posteriori Estimates Using Auxiliary Subspace Techniques.

In: JOURNAL OF SCIENTIFIC COMPUTING, Vol. 72, No. 1, 01.07.2017, p. 97-127.

Research output: Scientific - peer-reviewArticle

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@article{63a1a333b37a4deeb0c89527f8b20039,
title = "A Posteriori Estimates Using Auxiliary Subspace Techniques",
abstract = "A posteriori error estimators based on auxiliary subspace techniques for second order elliptic problems in Rd(d≥2) are considered. In this approach, the solution of a global problem is utilized as the error estimator. As the continuity and coercivity of the problem trivially leads to an efficiency bound, the main focus of this paper is to derive an analogous effectivity bound and to determine the computational complexity of the auxiliary approximation problem. With a carefully chosen auxiliary subspace, we prove that the error is bounded above by the error estimate up to oscillation terms. In addition, we show that the stiffness matrix of the auxiliary problem is spectrally equivalent to its diagonal. Several numerical experiments are presented verifying the theoretical results.",
keywords = "A posteriori error estimation, Finite element methods, High-order methods",
author = "Harri Hakula and Michael Neilan and Ovall, {Jeffrey S.}",
year = "2017",
month = "7",
doi = "10.1007/s10915-016-0352-0",
volume = "72",
pages = "97--127",
journal = "JOURNAL OF SCIENTIFIC COMPUTING",
issn = "0885-7474",
publisher = "Springer New York",
number = "1",

}

RIS - Download

TY - JOUR

T1 - A Posteriori Estimates Using Auxiliary Subspace Techniques

AU - Hakula,Harri

AU - Neilan,Michael

AU - Ovall,Jeffrey S.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - A posteriori error estimators based on auxiliary subspace techniques for second order elliptic problems in Rd(d≥2) are considered. In this approach, the solution of a global problem is utilized as the error estimator. As the continuity and coercivity of the problem trivially leads to an efficiency bound, the main focus of this paper is to derive an analogous effectivity bound and to determine the computational complexity of the auxiliary approximation problem. With a carefully chosen auxiliary subspace, we prove that the error is bounded above by the error estimate up to oscillation terms. In addition, we show that the stiffness matrix of the auxiliary problem is spectrally equivalent to its diagonal. Several numerical experiments are presented verifying the theoretical results.

AB - A posteriori error estimators based on auxiliary subspace techniques for second order elliptic problems in Rd(d≥2) are considered. In this approach, the solution of a global problem is utilized as the error estimator. As the continuity and coercivity of the problem trivially leads to an efficiency bound, the main focus of this paper is to derive an analogous effectivity bound and to determine the computational complexity of the auxiliary approximation problem. With a carefully chosen auxiliary subspace, we prove that the error is bounded above by the error estimate up to oscillation terms. In addition, we show that the stiffness matrix of the auxiliary problem is spectrally equivalent to its diagonal. Several numerical experiments are presented verifying the theoretical results.

KW - A posteriori error estimation

KW - Finite element methods

KW - High-order methods

UR - http://www.scopus.com/inward/record.url?scp=85008154381&partnerID=8YFLogxK

U2 - 10.1007/s10915-016-0352-0

DO - 10.1007/s10915-016-0352-0

M3 - Article

VL - 72

SP - 97

EP - 127

JO - JOURNAL OF SCIENTIFIC COMPUTING

T2 - JOURNAL OF SCIENTIFIC COMPUTING

JF - JOURNAL OF SCIENTIFIC COMPUTING

SN - 0885-7474

IS - 1

ER -

ID: 13637111