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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.

##### MSC:
 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
##### Keywords:
error estimates; finite element; non-smooth coefficients
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##### References:
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