Error bounds for semi-Galerkin approximations of nonhomogeneous incompressible fluids
P. Braz e Silva, M. A. Rojas-Medar
Abstract
We consider the spectral semi-Galerkin method applied to the nonhomogeneous Navier-Stokes equations. Under certain conditions it is known that the approximate solutions constructed through this method converge to a global strong solution of these equations. Here, we derive an optimal uniform in time error estimate in the H1 norm for the velocity. We also derive an error estimate for the density in some spaces Lr.
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