Ervin, V. J.; Shepherd, J. J. Numerical approximation of the Newtonian film blowing problem. (English) Zbl 1127.76008 Comput. Math. Appl. 49, No. 11-12, 1687-1707 (2005). Summary: We study the numerical approximation of a Newtonian model for film blowing. We prove that the approximations for the bubble radius, and the film thickness, converges to the true solution and establish the convergence rates. Numerical results are given which demonstrate the theoretical results obtained. Cited in 1 Document MSC: 76A20 Thin fluid films 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 76M10 Finite element methods applied to problems in fluid mechanics Keywords:film blowing; finite-element method; a priori error estimate PDF BibTeX XML Cite \textit{V. J. Ervin} and \textit{J. J. Shepherd}, Comput. Math. Appl. 49, No. 11--12, 1687--1707 (2005; Zbl 1127.76008) Full Text: DOI References: [1] Pearson, J.R.A.; Petrie, C.J.S., The flow of a tubular film. part 1: formal mathematical representation, J. fluid mech., 40, 1-19, (1970) · Zbl 0197.23801 [2] Pearson, J.R.A.; Petrie, C.J.S., The flow of a tubular film. part 2: interpretation of the model and discussion of solutions, J. fluid mech., 42, 609-625, (1970) · Zbl 0193.26201 [3] Han, C.D.; Park, J.Y., Studies on blown film extrusion I. experimental determination of elongational viscosity, J. appl. polym. sci., 19, 3257-3276, (1975) [4] Han, C.D.; Park, J.Y., Studies on blown film extrusion II. analysis of deformation and heat transfer processes, J. appl. polym. sci., 19, 3277-3290, (1975) [5] Han, C.D.; Park, J.Y., Studies on blown film extrusion III. bubble instability, J. appl. polym. sci., 19, 3291-3297, (1975) [6] Tam, D.C.H., Mathematical analysis of the blown Newtonian film, () [7] Doufas, A.K.; McHugh, A.J., Simulation of film blowing including flow-induced crystallization, J. rheol., 45, 1085-1104, (2001) [8] Sidiropoulos, V.; Tian, J.J.; Vlachopoulos, J., Computer simulation of film blowing, TAPPI journal, 79, 8, 113-118, (1996) [9] Johnson, C., Numerical solution of partial differential equations by the finite element method, (1987), Cambridge University Press [10] Brenner, S.C.; Scott, L.R., The mathematical theory of finite element methods, (1994), Springer-Verlag Publishing Cambridge · Zbl 0804.65101 [11] Luo, X.L.; Tanner, R.I., A computer study of film blowing, Polym. eng. sci., 25, 10, 620-629, (1985) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.