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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.

##### MSC:
 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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