A new class of nonparametric nonconforming quadrilateral finite elements is introduced which has the midpoint continuity and the mean value continuity at the interfaces of elements simultaneously as the rectangular DSSY element [J. Douglas, Jr., J.E. Santos, D. Sheen and X. Ye, 33 (1999) 747–770.] The parametric DSSY element for general quadrilaterals requires five degrees of freedom to have an optimal order of convergence [Z. Cai, J. Douglas, Jr., J.E. Santos, D. Sheen and X. Ye, 37 (2000) 253–254.],...
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
, 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...
We introduce a piecewise
-nonconforming quadrilateral finite element. First, we decompose a convex quadrilateral into the union of four triangles divided by its diagonals. Then the finite element space is defined by the set of all piecewise
-polynomials that are quadratic in each triangle and continuously differentiable on the quadrilateral. The degrees of freedom (DOFs) are defined by the eight values at the two Gauss points on each of the four edges plus the value...
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