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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
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References:
[1] Babuska, I.: Solution of interface problems by homogenization-1. SIAM J. Math. Anat.7, 603-634 (1976). · Zbl 0343.35022 · doi:10.1137/0507048
[2] Babuska, I., Osborn, J.E.: Analysis of finite element methods for second order boundary value problems using mesh dependent norms. Numer. Math.34, 41-62 (1980) · Zbl 0404.65055 · doi:10.1007/BF01463997
[3] Babuska, I., Osborn, J.E.: Generalized finite element methods: their performance and their relation to mixed methods. SIAM J Numer Anal.20, 510-536 (1983). · Zbl 0528.65046 · doi:10.1137/0720034
[4] Garg, S.K., Svalbomas, V., Gurtman, G.A.: Analysis of structural composite materials. New York: Marcel Dekker 1973.
[5] Nemat-Nasser, S.: Harmonic waves in layered composites. J. Appl. Mech.39, 850-852 (1972) · doi:10.1115/1.3422814
[6] Nemat-Nasser, S.: Generalized variational principles in non-linear and linear elasticity with applications, Mechanics Today, we. 1, pp.214-261. New York: Pergamon Press 1974 · Zbl 0305.73007
[7] Prosdorf, S., Schmidt, G.: A finite element collocation method for singular integral equations. Math. Nachr.100:33-60 (1981) · Zbl 0543.65089 · doi:10.1002/mana.19811000104
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