07-06
Nonconforming finite elements of higher order satisfying a modified compatibility condition
by Matthies, G.; Schieweck, F.
Preprint series: 07-06, Preprints
- MSC:
- 65N15 Error bounds
- 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
- 65N50 Mesh generation and refinement
Abstract: 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.
Keywords: nonconforming quadrilateral and hexahedral finite elements, multilevel grids, diffusion-convection-reaction equation, error estimates
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