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Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. II: Higher order FEM. (English) Zbl 0997.65127

[For part I see ibid. 71, No. 239, 945-969 (2002; reviewed above).]
This paper aims to establish the reliability and efficiency of local averaging. The authors consider the \(h\)-version of the conforming finite element method (FEM) of higher-order in two or three space dimensions. Three examples with uniform, adapted, and perturbed meshes and a variety of polynomial order FEMs conclude this paper.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations

Citations:

Zbl 0997.65126

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