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. 
@article{MZM_2005_78_6_a9,
     author = {V. V. Smagin},
     title = {On the {Rate} of {Convergence} of {Projection-Difference} {Methods} for {Smoothly} {Solvable} {Parabolic} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {907--918},
     publisher = {mathdoc},
     volume = {78},
     number = {6},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_6_a9/}
}
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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/