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...
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MDPI AG
2025-04-01
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| author | Christopher Provatidis Sascha Eisenträger |
| author_facet | Christopher Provatidis Sascha Eisenträger |
| author_sort | Christopher Provatidis |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f7fdecfeea5a431495f8fb2d29612d64 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-f7fdecfeea5a431495f8fb2d29612d642025-08-20T02:58:47ZengMDPI AGMathematics2227-73902025-04-01139149810.3390/math13091498Macroelement Analysis in T-Patches Using Lagrange PolynomialsChristopher Provatidis0Sascha Eisenträger1School of Mechanical Engineering, National Technical University of Athens, 15780 Zografou, GreeceInstitute of Materials, Technologies and Mechanics, Otto von Guericke University Magdeburg, 39106 Magdeburg, GermanyThis 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.https://www.mdpi.com/2227-7390/13/9/1498transfinite interpolationeliminationfinite element method |
| spellingShingle | Christopher Provatidis Sascha Eisenträger Macroelement Analysis in T-Patches Using Lagrange Polynomials Mathematics transfinite interpolation elimination finite element method |
| title | Macroelement Analysis in T-Patches Using Lagrange Polynomials |
| title_full | Macroelement Analysis in T-Patches Using Lagrange Polynomials |
| title_fullStr | Macroelement Analysis in T-Patches Using Lagrange Polynomials |
| title_full_unstemmed | Macroelement Analysis in T-Patches Using Lagrange Polynomials |
| title_short | Macroelement Analysis in T-Patches Using Lagrange Polynomials |
| title_sort | macroelement analysis in t patches using lagrange polynomials |
| topic | transfinite interpolation elimination finite element method |
| url | https://www.mdpi.com/2227-7390/13/9/1498 |
| work_keys_str_mv | AT christopherprovatidis macroelementanalysisintpatchesusinglagrangepolynomials AT saschaeisentrager macroelementanalysisintpatchesusinglagrangepolynomials |