Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
Jim Douglas Jr.; Santos, Juan E.; Sheen, Dongwoo; Ye, Xiu; Jim Douglas Jr. ; 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.; Santos Juan E.; 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.; Sheen Dongwoo; Department of Mathematics, Seoul National University, Seoul 151-742, Korea. Supported in part by KOSEF-GARC and BSRI-MOE-97.; Ye Xiu; Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR 72204-1099, USA.
Журнал:
ESAIM: Mathematical Modelling and Numerical Analysis
Дата:
1999
Аннотация:
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 <sub>1</sub>, 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 <sup>1</sup>(Ω) and in the Neumann and Robin cases in L <sup>2</sup>(Ω).
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