A parallel iterative Galerkin method based on nonconforming quadrilateral elements for second-order partial differential equations

  • Authors:

  • Yongdeok Kim;Sungyun Lee;Seki Kim

  • Affiliations:

  • Department of Mathematics, KAIST, Kusong-dong, Yusong-Gu, Taejon 305-701, South Korea;Department of Mathematics, KAIST, Kusong-dong, Yusong-Gu, Taejon 305-701, South Korea;Department of Mathematics, KAIST, Kusong-dong, Yusong-Gu, Taejon 305-701, South Korea

  • Venue:
  • Applied Mathematics and Computation
  • Year:
  • 2002

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Abstract

A parallel iterative Galerkin method based on domain decomposition technique with nonconforming quadrilateral finite elements will be analyzed for second-order elliptic equations subject to the Robin boundary condition. Optimal order error estimates are derived with respect to a broken H1-norm and L2-norm. Applications to time-dependent problems will be considered. Some numerical experiments supporting the theoretical results will be given. This paper is to extend the work in [J. Douglas Jr., J.E. Santos, D. Sheen, X. Ye, Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems, Mathematical Modelling and Numerical Analysis, RAIRO, Modél. Math. Anal. Numér. 33 (4) (1999) 747] to the non-self-adjoint case of second-order equations including the term b . ∇u. We suppose that uniformly ellipticity holds. Hence the arguments in (loc. cit.) may be applied, word for word. So some proofs will be omitted.