Geodesic
On the convergence velocity of Rothe's method for parabolic equation in noncylindric domain
Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 1, pp. 5-11.

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This article investigates the Rothe's method for starting boundary value problem for the linear parabolic equation of the second order in the domain, the boundary of which depends on time. The estimates of the convergence are obtained. 
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P. V. Vinogradova; A. G. Zarubin. On the convergence velocity of Rothe's method for parabolic equation in noncylindric domain. Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 1, pp. 5-11. http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a1/

[1] E. Rothe, “Warmeleiturgsgleichung mit nichtconstanten koeffizienten”, Math. Ann., 104 (1931), 340–362 | DOI | MR | Zbl

[2] P. V. Vinogradova, A. G. Zarubin, “O metode Galerkina dlya kvazilineinykh parabolicheskikh uravnenii v netsilindricheskoi oblasti”, Dalnevost. mat. zhurn., 3:1 (2002), 3–17

[3] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967, 736 pp. | MR

[4] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964, 540 pp. | MR

[5] E. Bekkenbakh, R. Bellman, Neravenstva, Mir, M., 1965, 276 pp. | MR