Liu, Zhiqing; Yu, Haiyuan; Nie, Cunyun The error analysis of an asymptotic expansion method for jump coefficient elliptic scalar equations. (Chinese. English summary) Zbl 1265.65226 J. Math., Wuhan Univ. 32, No. 4, 745-752 (2012). Summary: This paper studies some elliptic PDEs with jump coefficients (or multi-scale characteristic). By using the asymptotic expansion method, we decompose the PDEs with multi-scale characteristic into several PDEs with smooth coefficients (or single-scale characteristic). The same order of error function as that of the classic linear FEM under \(\|\cdot\|_0\) norm is obtained, which shows that this method is effective. MSC: 65N15 Error bounds for boundary value problems involving PDEs 65N55 Multigrid methods; domain decomposition 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 35R05 PDEs with low regular coefficients and/or low regular data Keywords:asymptotic expansion method; multi-scale; single-scale; finite element method; error analysis; elliptic PDEs; jump coefficients PDFBibTeX XMLCite \textit{Z. Liu} et al., J. Math., Wuhan Univ. 32, No. 4, 745--752 (2012; Zbl 1265.65226)