an:06342219
Zbl 1391.35004
Surry, Claude
Historical developments of computing of the inhomogeneous Dirichlet problem in bidimensional or multidimensional domains
EN
Bull. Soc. Sci. Lett. ????d??, S??r. Rech. D??form. 63, No. 1, 33-41 (2013).
00331120
2013
j
35-03 01A60 35J05 30C35 35A35
Dirichlet problem; flow profile; Dirichlet beam
Summary: We present the question of solving and computing nonhomogeneous Dirichlet problems in domains in \(\mathbb R^2\) or \(\mathbb R^n\) (\(n \geq 2\)). Using complex analysis we present the Kutta-Joukowski method of computing a bidimensional flow around a profile. In the case [\textit{G. K. Batchelor}, An introduction to fluid dynamics. 2nd pbk-ed. Cambridge: Cambridge University Press (1999; Zbl 0958.76001); \textit{L. D. Landau} and \textit{E. M. Lifshits}, Fluid mechanics. 2nd ed. Transl. from the Russian by J. B. Sykes and W. H. Reid. Oxford etc.: Pergamon Press (1987; Zbl 0655.76001)] of a three-dimensional flow around a cylindrical profile, we determine Sobolev spaces concerned and calculate by optimization methods an approximation of the solution by the use of Galerkin approximations [\textit{M. Chipot}, Variational inequalities and flow in porous media. New York, NY: Springer (1984; Zbl 0544.76095); Elements of nonlinear analysis. Basel: Birkh??user (2000; Zbl 0964.35002); \textit{W. Rudin}, Real and complex analysis. 2nd ed. McGraw-Hill Series in Higher Mathematics. New York etc.: McGraw-Hill Book Comp. XII, 452 p. (1974; Zbl 0278.26001)]. This problem arises in engineering science, thermal physics or dynamics of flows in porous media [Zbl 0544.76095; \textit{R. A. Silverman}, Complex analysis with applications. Englewood Cliffs, N. J.: Prentice-Hall, Inc. X, 274 p. (1974: Zbl 0348.30001)].
Zbl 0958.76001; Zbl 0655.76001; Zbl 0544.76095; Zbl 0964.35002; Zbl 0278.26001; Zbl 0348.30001