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Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems

Published online by Cambridge University Press:  15 August 2002

Jim Douglas Jr. ,
Juan E. Santos ,
Dongwoo Sheen  and
Xiu Ye
Jim Douglas Jr.
Affiliation:
Center for Applied Mathematics, Purdue University, West Lafayette, IN 47907-1395, USA. Supported in part by the NSF and the ONR. douglas@math.purdue.edu.
Juan E. Santos
Affiliation:
Center for Applied Mathematics, Purdue University, West Lafayette, IN 47907-1395, USA, and CONICET, Observatorio Astronomico, Universidad Nacional de La Plata, La Plata 1900, Argentina.
Dongwoo Sheen
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea. Supported in part by KOSEF-GARC and BSRI-MOE-97.
Xiu Ye
Affiliation:
Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR 72204-1099, USA.
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Abstract

Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions. Both simplicial and rectangular elements will be considered in two and three dimensions. The simplicial elements will be based on P 1, as for conforming elements; however, it is necessary to introduce new elements in the rectangular case. Optimal order error estimates are demonstrated in all cases with respect to a broken norm in H 1(Ω) and in the Neumann and Robin cases in L 2(Ω).

Keywords

Nonconforming Galerkin methodsquadrilateral elementssecond order elliptic problemsdomain decomposition iterative methods.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 4 , July 1999 , pp. 747 - 770
Copyright
© EDP Sciences, SMAI, 1999

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