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Lower norm error estimates for approximate solutions of differential equations with non-smooth coefficients. (English) Zbl 0613.65087
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 I. Babuška and 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.

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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