Geodesic
Weighted estimate for the convergence rate of a projection difference scheme for a quasilinear parabolic equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1294-1307

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A novel technique is proposed for analyzing the convergence of a projection difference scheme as applied to the initial value problem for a quasilinear parabolic operator-differential equation with initial data $u_0\in H$. The technique is based on the smoothing property of solutions to the differential problem for $t>0$. Under certain conditions on the nonlinear term, a new estimate of order $O(\sqrt\tau+h)$ for the convergence rate in a weighted energy norm is obtained without using a priori assumptions on the additional smoothness of weak solutions. 
@article{ZVMMF_2011_51_7_a9,
     author = {V. A. Grebennikov and A. V. Razgulin},
     title = {Weighted estimate for the convergence rate of a~projection difference scheme for a~quasilinear parabolic equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1294--1307},
     publisher = {mathdoc},
     volume = {51},
     number = {7},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a9/}
}
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V. A. Grebennikov; A. V. Razgulin. Weighted estimate for the convergence rate of a projection difference scheme for a quasilinear parabolic equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1294-1307. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a9/