The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version
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.
scientific article; zbMATH DE number 3994956
scientific article