A Posteriori Error Estimates for Maxwell’s Eigenvalue Problem

Daniele Boffi; Lucia Gastaldi; Rodolfo Rodríguez; Ivana Šebestová

doi:10.1007/s10915-018-0808-5

A Posteriori Error Estimates for Maxwell’s Eigenvalue Problem

Daniele Boffi, Lucia Gastaldi, Rodolfo Rodríguez, Ivana Šebestová

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

14 Scopus citations

Abstract

We introduce a residual error indicator for the Nédélec finite element approximation of the eigenmodes of the Maxwell cavity problem. By using the known equivalence with a mixed problem we prove reliability and efficiency of the error indicator. Numerical results confirm the optimal behavior of an adaptive scheme based on the error indicator.

Original language	English (US)
Pages (from-to)	1250-1271
Number of pages	22
Journal	Journal of Scientific Computing
Volume	78
Issue number	2
DOIs	https://doi.org/10.1007/s10915-018-0808-5
State	Published - Feb 15 2019
Externally published	Yes

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Generated from Scopus record by KAUST IRTS on 2020-05-05

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10.1007/s10915-018-0808-5

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title = "A Posteriori Error Estimates for Maxwell{\textquoteright}s Eigenvalue Problem",

abstract = "We introduce a residual error indicator for the N{\'e}d{\'e}lec finite element approximation of the eigenmodes of the Maxwell cavity problem. By using the known equivalence with a mixed problem we prove reliability and efficiency of the error indicator. Numerical results confirm the optimal behavior of an adaptive scheme based on the error indicator.",

author = "Daniele Boffi and Lucia Gastaldi and Rodolfo Rodr{\'i}guez and Ivana {\v S}ebestov{\'a}",

note = "Generated from Scopus record by KAUST IRTS on 2020-05-05",

year = "2019",

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AU - Boffi, Daniele

AU - Gastaldi, Lucia

AU - Rodríguez, Rodolfo

AU - Šebestová, Ivana

N1 - Generated from Scopus record by KAUST IRTS on 2020-05-05

PY - 2019/2/15

Y1 - 2019/2/15

N2 - We introduce a residual error indicator for the Nédélec finite element approximation of the eigenmodes of the Maxwell cavity problem. By using the known equivalence with a mixed problem we prove reliability and efficiency of the error indicator. Numerical results confirm the optimal behavior of an adaptive scheme based on the error indicator.

AB - We introduce a residual error indicator for the Nédélec finite element approximation of the eigenmodes of the Maxwell cavity problem. By using the known equivalence with a mixed problem we prove reliability and efficiency of the error indicator. Numerical results confirm the optimal behavior of an adaptive scheme based on the error indicator.

UR - http://link.springer.com/10.1007/s10915-018-0808-5

UR - http://www.scopus.com/inward/record.url?scp=85053433771&partnerID=8YFLogxK

U2 - 10.1007/s10915-018-0808-5

DO - 10.1007/s10915-018-0808-5

M3 - Article

SN - 0885-7474

VL - 78

SP - 1250

EP - 1271

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 2

ER -

A Posteriori Error Estimates for Maxwell’s Eigenvalue Problem

Abstract

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