Summary
Maximum-norm stability and error estimates of best approximation and nonsmooth data types are derived for the approximate solution of a parabolic equation in one space variable, using the continuous in time Galerkin method based on piecewise polynomial approximating functions on a quasi-uniform mesh.
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Thomée, V., Wahlbin, L.B. Maximum-norm stability and error estimates in Galerkin methods for parabolic equations in one space variable. Numer. Math. 41, 345–371 (1983). https://doi.org/10.1007/BF01418330
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DOI: https://doi.org/10.1007/BF01418330