A posteriori error bounds for classical and mixed FEM's for 4th-order elliptic equations with piece wise constant reaction coefficient having large jumps

Standard

A posteriori error bounds for classical and mixed FEM's for 4^th-order elliptic equations with piece wise constant reaction coefficient having large jumps. / Korneev, V.

в: Journal of Physics: Conference Series, Том 1715, № 1, 012030, 04.01.2021.

Результаты исследований: Научные публикации в периодических изданиях › статья в журнале по материалам конференции › Рецензирование

BibTeX

@article{45593cc41a9146368dce018ee16a2aac,

title = "A posteriori error bounds for classical and mixed FEM's for 4th-order elliptic equations with piece wise constant reaction coefficient having large jumps",

abstract = "We present guaranteed, robust and computable a posteriori error bounds for approximate solutions of the equation ∆∆u + κ2u = f by classical and mixed Ciarlet-Raviart finite element methods. We concentrate on the case when the reaction coefficient κ2 is subdomain (finite element) wise constant and chaotically varies between subdomains in the sufficiently wide range. It is proved that the bounds for the classical FEM's are robust with respect to κ ∈ [0, ch−2], where c = const and h is the maximal size of finite elements, and possess additional useful features. The coefficients in fronts of two typical norms in their right parts only insignificantly worse than those for κ ≡ const, and the bounds can be calculated without resorting to the equilibration procedures. Besides, they are sharp at least for low order methods, if the testing moments and deflection in their right parts are found by accurate recovery procedures. The technique of derivation of the bounds is based on the approach similar to one used in our preceding papers for simpler problems.",

author = "V. Korneev",

note = "Publisher Copyright: {\textcopyright} 2021 Institute of Physics Publishing. All rights reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.; International Conference on Marchuk Scientific Readings 2020, MSR 2020 ; Conference date: 19-10-2020 Through 23-10-2020",

year = "2021",

month = jan,

day = "4",

doi = "10.1088/1742-6596/1715/1/012030",

language = "English",

volume = "1715",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing Ltd.",

number = "1",

}

RIS

TY - JOUR

T1 - A posteriori error bounds for classical and mixed FEM's for 4th-order elliptic equations with piece wise constant reaction coefficient having large jumps

AU - Korneev, V.

PY - 2021/1/4

Y1 - 2021/1/4

N2 - We present guaranteed, robust and computable a posteriori error bounds for approximate solutions of the equation ∆∆u + κ2u = f by classical and mixed Ciarlet-Raviart finite element methods. We concentrate on the case when the reaction coefficient κ2 is subdomain (finite element) wise constant and chaotically varies between subdomains in the sufficiently wide range. It is proved that the bounds for the classical FEM's are robust with respect to κ ∈ [0, ch−2], where c = const and h is the maximal size of finite elements, and possess additional useful features. The coefficients in fronts of two typical norms in their right parts only insignificantly worse than those for κ ≡ const, and the bounds can be calculated without resorting to the equilibration procedures. Besides, they are sharp at least for low order methods, if the testing moments and deflection in their right parts are found by accurate recovery procedures. The technique of derivation of the bounds is based on the approach similar to one used in our preceding papers for simpler problems.

AB - We present guaranteed, robust and computable a posteriori error bounds for approximate solutions of the equation ∆∆u + κ2u = f by classical and mixed Ciarlet-Raviart finite element methods. We concentrate on the case when the reaction coefficient κ2 is subdomain (finite element) wise constant and chaotically varies between subdomains in the sufficiently wide range. It is proved that the bounds for the classical FEM's are robust with respect to κ ∈ [0, ch−2], where c = const and h is the maximal size of finite elements, and possess additional useful features. The coefficients in fronts of two typical norms in their right parts only insignificantly worse than those for κ ≡ const, and the bounds can be calculated without resorting to the equilibration procedures. Besides, they are sharp at least for low order methods, if the testing moments and deflection in their right parts are found by accurate recovery procedures. The technique of derivation of the bounds is based on the approach similar to one used in our preceding papers for simpler problems.

UR - http://www.scopus.com/inward/record.url?scp=85100775979&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1715/1/012030

DO - 10.1088/1742-6596/1715/1/012030

M3 - Conference article

AN - SCOPUS:85100775979

VL - 1715

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012030

T2 - International Conference on Marchuk Scientific Readings 2020, MSR 2020

Y2 - 19 October 2020 through 23 October 2020

ER -

ID: 74304253