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Nonconforming finite elements of higher order satisfying a modified compatibility condition

by Matthies, G., Schieweck, F..

Series: 2007-06, Preprints

65N15 Error bounds
65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
65N50 Mesh generation and refinement

For a general diffusion-convection-reaction equation,
we analyze families of nonconforming
finite elements of arbitrary order on a sequence of multilevel grids
consisting of quadrilaterals or hexahedra.
We prove existence and uniqueness of the discrete solution and
optimal order of convergence in the broken $H^1$-seminorm and
the $L^2$-norm.
The novelty of our approach is that
the usual integral compatibility condition of the discrete functions
across the element faces is modified such that it
can be solely treated on the
reference element once for all faces of the grid.
A numerical comparison between
conforming and nonconforming discretizations will be given in the
three-dimensional case.

nonconforming quadrilateral and hexahedral finite elements, multilevel grids, diffusion-convection-reaction equation, error estimates