We consider the Galerkin method to solve a parabolic initial boundary value problem in one space variable, using piecewise polynomial functions and give an alternative proof of superconvergence. Then by means of Lobatto quadrature, we obtain purely explicit vector initial value problems without loss in the order of accuracy, global or pointwise.
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SIAM Journal on Numerical Analysis
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Bakker, M. (1980). On the numerical solution of parabolic equations in a single space variable by the continuous time galerkin method. SIAM Journal on Numerical Analysis, 17(1), 162–177.