Premium
Finite element solutions for an equilateral triangle
Author(s) -
Daly P.
Publication year - 1974
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620080305
Subject(s) - equilateral triangle , mathematics , mathematical analysis , boundary (topology) , grid , finite element method , node (physics) , boundary value problem , homogeneous , polynomial , finite difference , geometry , combinatorics , physics , quantum mechanics , thermodynamics
In a two‐dimensional space of points on an equilateral triangle grid, a single difference equation holding at each node is found from the finite element formulation of the wave equation for all published polynomial orders of the functional expansion. Assuming homogeneous boundary conditions on any equilateral triangle whose edges and vertices pass through the grid points, the eigensolutions of the difference equation are found exactly and thus provide an excellent test problem for the programmer or engineer. The advantage of the present method over other formulations is that the number of linear operations required to produce the difference equation is minimal.