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Second order accurate up to the axis of symmetry finite element iteration methods with splitting of boundary conditions for the Stokes and the like systems in a spherical layer. (Russian, English) Zbl 1095.35029

Zh. Vychisl. Mat. Mat. Fiz. 45, No. 5, 846-889 (2005); translation in Comput. Math. Math. Phys. 45, No. 5, 816-857 (2005).
For the Stokes and Stokes-type systems the finite element linear approximations of the Laplace-Beltrami operator are constructed with splitting of the boundary conditions. For iterations at spherical coordinate system and spherical layer there are used one-dimensional three-diagonal operators for angular and for radial variables, thus enhancing the computation program efficiency. The second order of accuracy is demonstrated with respect to the mesh width both for velocity and pressure values. At large values of the singular parameter some losses of accuracy of the pressure computations are mentioned.

MSC:

35Q30 Navier-Stokes equations
76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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