Lower norm error estimates for approximate solutions of differential equations with non-smooth coefficients (Q1819550)

We derive error estimates in \(L_ p\)-norm, \(1\leq p\leq \infty\), for the \(L_ 2\)-finite element approximation to solutions of boundary value problems, where the coefficients are functions of bounded variation. The \(L_ 2\)-finite element method was introduced by \textit{I. Babuška} and \textit{J. Osborn} [SIAM J. Numer. Anal. 20, 510-536 (1983; Zbl 0528.65046)] and was shown to be effective for problems with non-smooth coefficients.