Abstract:
The concept of an $R_{\nu}$-generalized solution of the Oseen problem in a skew-symmetric form in weighted sets in a polygonal two-dimensional domain with an incoming angle on the boundary is defined. Thanks to such a solution definition of the problem, it is possible to construct a weighted finite element method. A method for finding an approximate solution to the problem without loss of accuracy. In this case, it is possible to obtain the convergence rate of an approximate solution to the exact one of the problem that is independent of the magnitude of the incoming angle on the boundary of the domain. In the paper, relations that connect the norms of functions in special sets with bilinear forms in an asymmetric variational formulation of the problem with an angular singularity are established. The existence and uniqueness of the $R_{\nu}$-generalized solution in weighted sets is proved.
Keywords:angular singularity, Oseen problem in skew-symmetric form, $R_{\nu}$-generalized solution.
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