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).