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Optimal error estimates for linear parabolic problems under minimal regularity assumptions

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Abstract

We study the approximation of linear parabolic problems by means of Galerkin approximation in space and θ-method in time. The error is evaluated in norms of typeH δ t (H x1 ) ⋂H δ+1/2 t (L 2 x ) for |δ|≤1/2. We prove error estimates which are optimal with respect to the regularity assumptions on the right-hand side of the equation.

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Dedicated to Professor Aldo Ghizzetti on his 75th birthday

Istituto di Analisi Numerica del C.N.R.

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Baiocchi, C., Brezzi, F. Optimal error estimates for linear parabolic problems under minimal regularity assumptions. Calcolo 20, 143–176 (1983). https://doi.org/10.1007/BF02575590

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  • DOI: https://doi.org/10.1007/BF02575590

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