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On very accurate enclosure of the optimal constant in the a priori error estimates for \(H_0^2\)-projection. (English) Zbl 1190.65166
Authors’ abstract: We present constructive a priori error estimates for \(H_0^2\)-projection into a space of polynomials on a one-dimensional interval. Here, “constructive” indicates that we can obtain the error bounds in which all constants are explicitly given or are represented in a numerically computable form. Using the properties of Legendre polynomials, we consider a method by which to determine these constants to be as small as possible. Using the proposed technique, the optimal constant could be enclosed in a very narrow interval with result verification.
Furthermore, constructive error estimates for finite element \(H_0^2\)-projection in one dimension are presented. These types of estimates will play an important role in the numerical verification of solutions for nonlinear fourth-order elliptic problems as well as in the guaranteed a posteriori error analysis for the finite element method or the spectral method.

MSC:
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J40 Boundary value problems for higher-order elliptic equations
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