Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
Center for Applied Mathematics, Purdue
University, West Lafayette, IN 47907-1395, USA. Supported in part by the
NSF and the ONR. email@example.com.
2 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.
3 Department of Mathematics, Seoul National University, Seoul 151-742, Korea. Supported in part by KOSEF-GARC and BSRI-MOE-97.
4 Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR 72204-1099, USA.
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 P1, 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 H1(Ω) and in the Neumann and Robin cases in L2(Ω).
Mathematics Subject Classification: 65N30
Key words: Nonconforming Galerkin methods / quadrilateral elements / second order elliptic problems / domain decomposition iterative methods.
© EDP Sciences, SMAI, 1999