Very Weak Estimates for a Rough Poisson-Dirichlet Problem with Natural Vertical Boundary Conditions
Milišić, Vuk
Methods Appl. Anal., Tome 16 (2009) no. 1, p. 157-186 / Harvested from Project Euclid
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This work is a continuation of [3]; it deals with rough boundaries in the simplified context of a Poisson equation. We impose Dirichlet boundary conditions on the periodic microscopic perturbation of a flat edge on one side and natural homogeneous Neumann boundary conditions are applied on the inlet/outlet of the domain. To prevent oscillations on the Neumann-like boundaries, we introduce a microscopic vertical corrector defined in a rough quarter-plane. In [3] we studied a priori estimates in this setting; here we fully develop very weak estimates à la Nečas [17] in the weighted Sobolev spaces on an unbounded domain. We obtain optimal estimates which improve those derived in [3]. We validate these results numerically, proving first order results for boundary layer approximation including the vertical correctors and a little less for the averaged wall-law introduced in the literature [13, 18].
Publié le : 2009-06-15
Classification:  Wall-laws,  rough boundary,  Laplace equation,  multi-scale modelling,  boundary layers,  error estimates,  natural boundary conditions,  vertical boundary correctors,  76D05,  35B27,  76Mxx,  65Mxx 
@article{1257170934,
     author = {Mili\v si\'c, Vuk},
     title = {Very Weak Estimates for a Rough Poisson-Dirichlet Problem with Natural Vertical
				Boundary Conditions},
     journal = {Methods Appl. Anal.},
     volume = {16},
     number = {1},
     year = {2009},
     pages = { 157-186},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1257170934}
}

Milišić, Vuk. Very Weak Estimates for a Rough Poisson-Dirichlet Problem with Natural Vertical
				Boundary Conditions. Methods Appl. Anal., Tome 16 (2009) no. 1, pp.  157-186. http://gdmltest.u-ga.fr/item/1257170934/