Global superconvergence in combinations of Ritz-Galerkin-FEM for singularity problems (Q1298791)

For seeking the corner singularity solution of an elliptic boundary value problem a combination of the piecewise bilinear element approximation and the singular function method is proposed. For different coupling strategies, such as the nonconforming constraints, the penalty integrals and the penalty plus hybrid integrals an estimation of the convergence rate is obtained. If \(h\) is the maximal boundary length of quasiuniform rectangles used and \(\delta>0\) is an arbitrarily small number, it can be proved that the global superconvergence rate is \(O(h^{2-\delta})\). A small effort in computation time is paid to conduct a posteriori interpolation of the numerical solution, only on the subregion used in the finite element methods (FEMs).