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

Carstensen, Carsten; Bartels, Sören

Math. Comput. 71, No. 239, 945-969 (2002).

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.

Reviewer: Pavol Chocholatý (Bratislava)

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

Keywords:

averaging technique; a posteriori error estimates; residual based error estimate; adaptive algorithm; reliability; finite element method; mixed finite element method; nonconforming finite element method; unstructured grids; superconvergence; numerical experiments; Laplace equation

Citations:

Zbl 0997.65127

Software:

na14

References:

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