Abstract
Error estimates are proved for the Galerkin procedure applied to initial value problems of “parabolic” type in Hilbert space without regularity requirements of the initial element. They are based on approximation assumptions for the Ritz operator of the associated “elliptic” problem. Approximation properties of this type are also shown to be necessary for the obtained error bounds.
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Helfrich, H.P. Fehlerabschätzungen für das Galerkinverfahren zur Lösung von Evolutionsgleichungen. Manuscripta Math 13, 219–235 (1974). https://doi.org/10.1007/BF01168227
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DOI: https://doi.org/10.1007/BF01168227