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Analysis of the cell vertex finite volume method for the Cauchy-Riemann equations

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Abstract
This paper initiates a study of finite volume methods for linear first-order elliptic systems by performing a stability and convergence analysis of the cell Vertex approximation of the Cauchy-Riemann equations. The approach is based on reformulating the scheme as a Petrov-Galerkin finite element method with continuous bilinear trial functions and piecewise constant test functions. Optimal error bounds are derived in a mesh-dependent norm, and the counting problem which may occur due to geometry and boundary conditions is considered.
Keywords
error analysis, ELEMENT, stability, finite volume, Cauchy-Riemann equations

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MLA
Vanmaele, Michèle, K William Morton, Endre Süli, et al. “Analysis of the Cell Vertex Finite Volume Method for the Cauchy-Riemann Equations.” SIAM JOURNAL ON NUMERICAL ANALYSIS 34.5 (1997): 2043–2062. Print.
APA
Vanmaele, Michèle, Morton, K. W., Süli, E., & Borzì, A. (1997). Analysis of the cell vertex finite volume method for the Cauchy-Riemann equations. SIAM JOURNAL ON NUMERICAL ANALYSIS, 34(5), 2043–2062.
Chicago author-date
Vanmaele, Michèle, K William Morton, Endre Süli, and Alfio Borzì. 1997. “Analysis of the Cell Vertex Finite Volume Method for the Cauchy-Riemann Equations.” Siam Journal on Numerical Analysis 34 (5): 2043–2062.
Chicago author-date (all authors)
Vanmaele, Michèle, K William Morton, Endre Süli, and Alfio Borzì. 1997. “Analysis of the Cell Vertex Finite Volume Method for the Cauchy-Riemann Equations.” Siam Journal on Numerical Analysis 34 (5): 2043–2062.
Vancouver
1.
Vanmaele M, Morton KW, Süli E, Borzì A. Analysis of the cell vertex finite volume method for the Cauchy-Riemann equations. SIAM JOURNAL ON NUMERICAL ANALYSIS. 1997;34(5):2043–62.
IEEE
[1]
M. Vanmaele, K. W. Morton, E. Süli, and A. Borzì, “Analysis of the cell vertex finite volume method for the Cauchy-Riemann equations,” SIAM JOURNAL ON NUMERICAL ANALYSIS, vol. 34, no. 5, pp. 2043–2062, 1997.
@article{273978,
  abstract     = {{This paper initiates a study of finite volume methods for linear first-order elliptic systems by performing a stability and convergence analysis of the cell Vertex approximation of the Cauchy-Riemann equations. The approach is based on reformulating the scheme as a Petrov-Galerkin finite element method with continuous bilinear trial functions and piecewise constant test functions. Optimal error bounds are derived in a mesh-dependent norm, and the counting problem which may occur due to geometry and boundary conditions is considered.}},
  author       = {{Vanmaele, Michèle and Morton, K William and Süli, Endre and Borzì, Alfio}},
  issn         = {{0036-1429}},
  journal      = {{SIAM JOURNAL ON NUMERICAL ANALYSIS}},
  keywords     = {{error analysis,ELEMENT,stability,finite volume,Cauchy-Riemann equations}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{2043--2062}},
  title        = {{Analysis of the cell vertex finite volume method for the Cauchy-Riemann equations}},
  url          = {{http://dx.doi.org/10.1137/S0036142994276384}},
  volume       = {{34}},
  year         = {{1997}},
}

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