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Extra resources for Advances in Chemical Physics: Proceedings of the Conference on Instability and Dissipative Strutures in Hydrodynamics, Volume 32
We further can prove that A question which is of great mathematical interest is the regularity of u in S. M . ROWDE 54 M+ and the smoothness of S (see for example Refs. 33 and 34). Boundary value problems such as these determined by the above variational formulation are known as unilateral boundary value problems. do. The finite dimensional problem corresponding to these problems25 is by no means trivial. The finite dimensional version of (27), for example, is to minimize the quadratic form J F o r linear elements if (p, > 0,1 < i < n then @“(x)2 0,x EM, that is, a certain “convexity” property is present.
We remark that with only 12 degrees of freedom (n = 3, m =1) more accurate results were obtained than with over 100 degrees of freedom and a lower order method! Extensive results and convergence studies for this problem are reported in Ref. 29. P Fig. 7. 0, y = 0. S. M. ROHDE 50 VI. LOCAL POTENTIAL FORMULATION FOR THE SLOW VISCOUS FLOW OF NON-NEWTONIAN FLUID BETWEEN NONPARALLEL PLATES The addition of highpolymers to ordinary mineral oils has been found to, in certain cases, radically change the macroscopic characteristics of that flow.
V. Application of the Local Potential Finite Element Iterative Scheme to the Slow Viscous Flow of a Compressible Fluid betweenFiniteEccentric Permeablecylinders . . . VI. Local Potential Formulation for the Slow Viscous Flow of Non-Newtonian Fluid between Nonparallel Plates . . VII. A Variational Formulation for Certain Free Boundary Problems . . . . . . . . . VIII. SomeParticular FreeBoundary Problems . . . IX. Applications to Stability Theory . . . . . X. Conclusions .