Adaptive IGAFEM with optimal convergence rates: T-splines

Gregor Gantner; Dirk Praetorius

doi:10.1016/j.cagd.2020.101906

Adaptive IGAFEM with optimal convergence rates: T-splines

Gregor Gantner^*
, Dirk Praetorius

^*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd degree on T-meshes generated by the refinement strategy of Morgenstern and Peterseim (2015) in 2D and Morgenstern (2016) in 3D. Adaptivity is driven by some weighted residual a posteriori error estimator. We prove linear convergence of the error estimator (which is equivalent to the sum of energy error plus data oscillations) with optimal algebraic rates with respect to the number of elements of the underlying mesh.

Original language	English
Article number	101906
Number of pages	20
Journal	Computer aided geometric design
Volume	81
Early online date	9 Jun 2020
DOIs	https://doi.org/10.1016/j.cagd.2020.101906
Publication status	Published - Aug 2020
Externally published	Yes

Keywords

Isogeometric analysis
T-splines
Adaptivity
Optimal convergence rates

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10.1016/j.cagd.2020.101906Licence: CC BY

ArticleFinal published version, 1.03 MBLicence: CC BY

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title = "Adaptive IGAFEM with optimal convergence rates: T-splines",

abstract = "We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd degree on T-meshes generated by the refinement strategy of Morgenstern and Peterseim (2015) in 2D and Morgenstern (2016) in 3D. Adaptivity is driven by some weighted residual a posteriori error estimator. We prove linear convergence of the error estimator (which is equivalent to the sum of energy error plus data oscillations) with optimal algebraic rates with respect to the number of elements of the underlying mesh.",

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author = "Gregor Gantner and Dirk Praetorius",

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year = "2020",

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doi = "10.1016/j.cagd.2020.101906",

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T1 - Adaptive IGAFEM with optimal convergence rates

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AU - Gantner, Gregor

AU - Praetorius, Dirk

PY - 2020/8

Y1 - 2020/8

N2 - We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd degree on T-meshes generated by the refinement strategy of Morgenstern and Peterseim (2015) in 2D and Morgenstern (2016) in 3D. Adaptivity is driven by some weighted residual a posteriori error estimator. We prove linear convergence of the error estimator (which is equivalent to the sum of energy error plus data oscillations) with optimal algebraic rates with respect to the number of elements of the underlying mesh.

AB - We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd degree on T-meshes generated by the refinement strategy of Morgenstern and Peterseim (2015) in 2D and Morgenstern (2016) in 3D. Adaptivity is driven by some weighted residual a posteriori error estimator. We prove linear convergence of the error estimator (which is equivalent to the sum of energy error plus data oscillations) with optimal algebraic rates with respect to the number of elements of the underlying mesh.

KW - Isogeometric analysis

KW - T-splines

KW - Adaptivity

KW - Optimal convergence rates

UR - https://www.scopus.com/pages/publications/85086144996

U2 - 10.1016/j.cagd.2020.101906

DO - 10.1016/j.cagd.2020.101906

M3 - Article

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VL - 81

JO - Computer aided geometric design

JF - Computer aided geometric design

M1 - 101906

ER -

Adaptive IGAFEM with optimal convergence rates: T-splines

Abstract

Keywords

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