Macroelement Analysis in T-Patches Using Lagrange Polynomials

This paper investigates the derivation of global shape functions in T-meshed quadrilateral patches through transfinite interpolation and local elimination. The same shape functions may be alternatively derived starting from a background tensor product of Lagrange polynomials and then imposing linear constraints. Based on the nodal points of the T-mesh, which are associated with the primary degrees of freedom (DOFs), all the other points of the background grid (i.e., the secondary DOFs) are interpolated along horizontal and vertical stations (isolines) of the tensor product, and thus linear relationships are derived. Implementing these constraints into the starting formula in the sense of a Schur complement reduction, the global shape functions associated with the primary degrees of freedom are created. The quality of the elements is verified by the numerical solution of a typical potential problem of second order, with boundary conditions of Dirichlet and Neumann type.