The method of auxiliary mapping for the finite element solutions of elliptic problems containing singularities
The method of auxiliary mapping (MAM) introduced by \textit{I. Babuška} and \textit{H.-S. Oh} [Numer. Methods Partial Differ. Equations 6, No. 4, 371-392 (1990; Zbl 0717.65084)], is applied to the homogeneous Laplace equation with boundary singularities and to the Helmholtz equation with both corner and boundary singularities. An exponential rate of convergence for the \(p\)-version of the finite element method (FEM) is proved. In addition, convergence estimates are proved for MAM applied to the \(h\)-\(p\) version of the FEM. Three benchmark problems are subject to numerical experiments comparing MAM with other FEM codes (PLTMG 6, FESOP), with ELLPACK, and the singular element code ISBFM. Errors and CPU time are compared graphically, as well.
scientific article; zbMATH DE number 516917