Geodesic
On the Rate of Convergence of Projection-Difference Methods for Smoothly Solvable Parabolic Equations
Matematičeskie zametki, Tome 78 (2005) no. 6, pp. 907-918.

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A linear parabolic problem in a separable Hilbert space is solved approximately by the projection-difference method. The problem is discretized in space by the Galerkin method orientated towards finite-dimensional subspaces of finite-element type and in time by using the implicit Euler method and the modified Crank–Nicolson scheme. We establish uniform (with respect to the time grid) and mean-square (in space) error estimates for the approximate solutions. These estimates characterize the rate of convergence of errors to zero with respect to both the time and space variables. 
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V. V. Smagin. On the Rate of Convergence of Projection-Difference Methods for Smoothly Solvable Parabolic Equations. Matematičeskie zametki, Tome 78 (2005) no. 6, pp. 907-918. http://geodesic.mathdoc.fr/item/MZM_2005_78_6_a9/

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