Development and Analysis of Higher Order Finite Volume Methods over Rectangles for Elliptic Equations

@article{Cai2003DevelopmentAA,
  title={Development and Analysis of Higher Order Finite Volume Methods over Rectangles for Elliptic Equations},
  author={Zhiqiang Cai and Jim Douglas and Moongyu Park},
  journal={Adv. Comput. Math.},
  year={2003},
  volume={19},
  pages={3-33}
}
Currently used finite volume methods are essentially low order methods. In this paper, we present a systematic way to derive higher order finite volume schemes from higher order mixed finite element methods. Mostly for convenience but sometimes from necessity, our procedure starts from the hybridization of the mixed method. It then approximates the inner product of vector functions by an appropriate, critical quadrature rule; this allows the elimination of the flux and Lagrange multiplier… CONTINUE READING

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Efficient rectangular mixed finite elements in two and three space variables

F. Brezzi, J. Douglas, Jr., M. Fortin, L. D. Marini
RAIRO Anal. Numér • 1987
View 6 Excerpts
Highly Influenced

Finite element and finite difference methods for continuous flows in porous media, in: The Mathematics of Reservoir Simulation, ed

T. F. Russell, M. F. Wheeler
1983
View 6 Excerpts
Highly Influenced

Connection between finite volume and mixed finite element methods, Modél

J. Baranger, J. F. Maitre, F. Oudin
Math. Anal. Numér • 1996
View 1 Excerpt

A new family of mixed finite element spaces over rectangles

J. Douglas, J. Wang
Mat . Apl . Comput . • 1993

A new family of mixed finite element spaces over rectangles, Mat

J. Douglas, Jr., J. Wang
Apl. Comput • 1993
View 1 Excerpt

Mixed and Hybrid Finite Element Methods (Springer

F. Brezzi, M. Fortin
New York, • 1991
View 2 Excerpts

On the finite volume element method

Z. Cai
Numer. Math • 1991
View 1 Excerpt

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