Convergence Analysis for a Nonsymmetric Galerkin Method for a Class of Singular Boundary Value Problems in One Space Dimension

摘要

A nonsymmetric Galerkin type piecewise polynomial approximation procedure for a class of singular boundary value problems in one space dimension is extended to the case of mildly nonlinear problems with the same type of singularity. The discretization of the stationary problem is analyzed with respect to super convergence properties at the nodal points. To obtain full superconvergence at all nodal points local mesh refinements must be introduced, even though the exact solution is smooth for the given class of problems.