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The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version. (English) Zbl 0614.65088
The p-version of the finite element method fixes the mesh and the convergence is obtained by increase of the degree of elements. This paper realizes an error analysis of this FEM version considering the most simple one-dimensional bilocal problem when its solution has a singularity of \(x^{\alpha}\)-type. The analysis is made in the more general frame of the best \(L_ 2\)-approximation of analytic functions which have a singularity of this type. Some numerical results confirm the accuracy of the estimates and show the performance of the p-version.
Reviewer: C.-I.Gheorghiu

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
30E10 Approximation in the complex plane
41A50 Best approximation, Chebyshev systems
34B05 Linear boundary value problems for ordinary differential equations
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