Estimate of the Convergence Rate of Finite Element Solutions to Elliptic Equations of Second Order with Discontinuous Coefficients

Abstract

In this paper, we consider elliptic boundary value problems with discontinuous coefficients and obtain the asymptotic optimal error estimate $\Vert u-u_k{\Vert }_{1,\Omega }⩽Ch|\ln h{|}^{1/2}\Vert u{\Vert }_{2,{\Omega }_1+{\Omega }_2}$ for triangle linear elements.

This is the English translation of the following paper: Jinchao Xu, \emph{Estimate of the Convergence Rate of Finite Element Solutions to Elliptic Equations of Second Order with Discontinuous Coefficients}, Natural Science Journal of Xiangtan University, No. 1, 1-5, 1982

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