Macroelement Analysis in T-Patches Using Lagrange Polynomials

Christopher Provatidis () and Sascha Eisenträger
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Christopher Provatidis: School of Mechanical Engineering, National Technical University of Athens, 15780 Zografou, Greece
Sascha Eisenträger: Institute of Materials, Technologies and Mechanics, Otto von Guericke University Magdeburg, 39106 Magdeburg, Germany

Mathematics, 2025, vol. 13, issue 9, 1-39

Abstract: 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. By implementing these constraints into the original formula/expression, global shape functions, which are only associated with primary DOFs, 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.

Keywords: transfinite interpolation; elimination; finite element method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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