E, Weinan; Huang, Hongci; Han, Weimin Error analysis of local refinements of polygonal domains. (English) Zbl 0625.65094 J. Comput. Math. 5, 89-94 (1987). This paper presents a thorough analysis of the local refinements of polygonal domains using weighted Sobolev spaces. The estimates obtained indicate the dependence of the approximation properties on the singularities of the solution. Theorems are presented for the existence and an estimation of the error in the solution. Reviewer: P.K.Mahanti Cited in 1 Document MSC: 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs Keywords:convergence rates; finite element method; local refinements of polygonal domains PDFBibTeX XMLCite \textit{W. E} et al., J. Comput. Math. 5, 89--94 (1987; Zbl 0625.65094)