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On residual-based a posteriori error estimation in hp-FEM. (English) Zbl 0991.65111
The Clément/Scott-Zhang interpolation operator is generalized to the hp-context and using this approach a new method of so-called polynomial inverse estimates is suggested. Using this method a family \(\eta_\alpha\), \(\alpha\in\langle 0,1\rangle\) of residual based error indicators for the hp-version of the finite element method (FEM) is presented and analyzed. Upper and lower bounds for these error indicators \(\eta_\alpha\) are estabilished and the hp-adaptive strategy is proposed. Some numerical examples for the illustration of the performance of error indicators and the adaptive strategy are also presented.

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