Geodesic
Strong-norm error estimates for the projective-difference method for approximately solving abstract parabolic equations
Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 898-909

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Solutions continuously differentiable with respect to time of parabolic equations in Hilbert space are obtained by the projective-difference method approximately. The discretization of the problem is carried out in the spatial variables using Galerkin's method, and in the time variable using Euler's implicit method. Strong-norm error estimates for approximate solutions are obtained. These estimates not only allow one to establish the convergence of the approximate solutions to the exact ones but also yield numerical characteristics of the rates of convergence. In particular, order-sharp error estimates for finite element subspaces are obtained. 
@article{MZM_1997_62_6_a10,
     author = {V. V. Smagin},
     title = {Strong-norm error estimates for the projective-difference method for approximately solving abstract parabolic equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {898--909},
     publisher = {mathdoc},
     volume = {62},
     number = {6},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_6_a10/}
}
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V. V. Smagin. Strong-norm error estimates for the projective-difference method for approximately solving abstract parabolic equations. Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 898-909. http://geodesic.mathdoc.fr/item/MZM_1997_62_6_a10/