Global superconvergence of simplified hybrid combinations of the Ritz--Galerkin and FEMs for elliptic equations with singularities. II: Lagrange elements and Adini's elements (Q1862002)

This paper presents a development of part I by \textit{Z. C. Li} [Computing 65, No. 1, 27-44 (2000; Zbl 0962.65088)] in high accurate solutions for the general case of the Poisson problems on a polygonal domain. It concerns elliptic boundary problems with singularities. Simplified hybrid combinations of the Ritz-Galerkin method and the finite element method are used to lead to global superconvergence rates on the entire solution domain. The solution domain is split into a singular subdomain with a singular point and a regular subdomain where the true solution is smooth enough. In the regular subdomain either the \(k\)-order Lagrange rectangles or Adini's elements are adapted. Numerical experiments are provided for combinations of Ritz-Galerkin and Adini's methods.