Approximations on Convex Star-Type Manifolds

The construction of approximations on radial ring grids on a circle and on a sphere is considered. In this case, to construct approximations, the values of the function at the grid nodes and the basis functions are required. Particular attention is given to the development of an algorithm for the sufficiently fine refinement of surface triangulation and the implementation of Courant-type approximations on a sphere and on a sphere with a cutout. The proposed refinement algorithm overcomes limitations associated with computer system memory. An algorithm for constructing a triangulation on a surface is described. Courant-type approximations are constructed on a sphere with and without a cutout.