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\(hp\)-interpolation of nonsmooth functions and an application to \(hp\)-a posteriori error estimation. (English) Zbl 1087.65108
The author develops an optimal quasi-interpolation operators suitable for an application in the framework of the \(hp\)-version of the finite element method. Two kinds of operators are used for preserving piecewise polynomial boundary conditions. It is shown that both operators achieve optimal convergence. No numerical experiments are presented for illustration. It is an interesting paper for a theoretical foundation.

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
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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