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An improved error estimate of the one-order asymptotic expansion for elliptic problems. (Chinese. English summary) Zbl 1174.65512
Summary: This paper carries out the error analysis of the asymptotic expansion proposed the authors [Acta Math. Appl. Sin. 22, No. 1, 38–46 (1999; Zbl 0963.35185); Numer. Math. 96, No. 3, 525–581 (2004; Zbl 1049.65126)] for elliptic problems. In particular, we show that the first asymptotic solution is convergent with order $$O(\varepsilon)$$ provided that the coefficients satisfy some symmetric properties proposed in [op. cit.].
##### MSC:
 65N15 Error bounds for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods 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