First-order system least squares on curved boundaries: Higher-order Raviart-Thomas elements

Fleurianne Bertrand; Steffen Münzenmaier; Gerhard Starke

doi:10.1137/130948902

First-order system least squares on curved boundaries: Higher-order Raviart-Thomas elements

Fleurianne Bertrand, Steffen Münzenmaier, Gerhard Starke

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

16 Citations (Scopus)

Abstract

With this paper, our investigation of the finite element approximation on curved boundaries using Raviart-Thomas spaces in the context of first-order system least squares methods is continued and extended to the higher-order case. It is shown that the optimal order of convergence is retained from the lowest-order case if a parametric version of Raviart-Thomas elements is used. This is illustrated numerically for an elliptic boundary value problem involving a circular boundary curve.

Original language	English
Pages (from-to)	3165-3180
Number of pages	16
Journal	SIAM Journal on Numerical Analysis
Volume	52
Issue number	6
DOIs	https://doi.org/10.1137/130948902
Publication status	Published - 2014
Externally published	Yes

Keywords

Firstorder system least squares
Interpolated boundaries
Parametric finite elements
Raviart-Thomas spaces

Access to Document

10.1137/130948902

Cite this

@article{38bf5a8692b346de8d1de75368878a13,

title = "First-order system least squares on curved boundaries: Higher-order Raviart-Thomas elements",

abstract = "With this paper, our investigation of the finite element approximation on curved boundaries using Raviart-Thomas spaces in the context of first-order system least squares methods is continued and extended to the higher-order case. It is shown that the optimal order of convergence is retained from the lowest-order case if a parametric version of Raviart-Thomas elements is used. This is illustrated numerically for an elliptic boundary value problem involving a circular boundary curve.",

keywords = "Firstorder system least squares, Interpolated boundaries, Parametric finite elements, Raviart-Thomas spaces",

author = "Fleurianne Bertrand and Steffen M{\"u}nzenmaier and Gerhard Starke",

year = "2014",

doi = "10.1137/130948902",

language = "English",

volume = "52",

pages = "3165--3180",

journal = "SIAM Journal on Numerical Analysis",

issn = "0036-1429",

publisher = "Society for Industrial and Applied Mathematics",

number = "6",

}

TY - JOUR

T1 - First-order system least squares on curved boundaries

T2 - Higher-order Raviart-Thomas elements

AU - Bertrand, Fleurianne

AU - Münzenmaier, Steffen

AU - Starke, Gerhard

PY - 2014

Y1 - 2014

N2 - With this paper, our investigation of the finite element approximation on curved boundaries using Raviart-Thomas spaces in the context of first-order system least squares methods is continued and extended to the higher-order case. It is shown that the optimal order of convergence is retained from the lowest-order case if a parametric version of Raviart-Thomas elements is used. This is illustrated numerically for an elliptic boundary value problem involving a circular boundary curve.

AB - With this paper, our investigation of the finite element approximation on curved boundaries using Raviart-Thomas spaces in the context of first-order system least squares methods is continued and extended to the higher-order case. It is shown that the optimal order of convergence is retained from the lowest-order case if a parametric version of Raviart-Thomas elements is used. This is illustrated numerically for an elliptic boundary value problem involving a circular boundary curve.

KW - Firstorder system least squares

KW - Interpolated boundaries

KW - Parametric finite elements

KW - Raviart-Thomas spaces

UR - http://www.scopus.com/inward/record.url?scp=84919664326&partnerID=8YFLogxK

U2 - 10.1137/130948902

DO - 10.1137/130948902

M3 - Article

AN - SCOPUS:84919664326

VL - 52

SP - 3165

EP - 3180

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 6

ER -

First-order system least squares on curved boundaries: Higher-order Raviart-Thomas elements

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this