## Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. I: Low order conforming, nonconforming, and mixed FEM.(English)Zbl 0997.65126

This paper deals with the robust reliability of all averaging techniques, robust with respect to violated (local) symmetry of meshes and superconvergence and robust with respect to other boundry conditions or other finite element methods (FEMs). Basic estimates re provided for a local and global averaging technique and their equivalence. The consequences to averaging techniques uses in a posteriori error control for first-order conforming, nonconforming and mixed finite element schemes are presented. The theoretical results are supported by numerical experiments for the Lapalce equation with mixed boundary conditions.

### MSC:

 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Zbl 0997.65127

na14
Full Text:

### References:

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