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

• Published in: Applied mathematics and computation Vol. 127; no. 2; pp. 387 - 404
• Main Authors: Kim, Yongdeok, Lee, Sungyun, Kim, Seki
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.04.2002; Elsevier
• Subjects: Domain decomposition methods; Elliptic problems; Exact sciences and technology; Mathematics; Nonconforming methods; Parallel iterative methods; Sciences and techniques of general use; Elliptic problems; Domain decomposition methods; Parallel iterative methods; Nonconforming methods
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/S0096-3003(01)00018-2

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 H 1-norm and L 2-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.