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Triangular finite elements for the generalized Bessel equation of order m
Author(s) -
Konrad A.,
Silvester P.
Publication year - 1973
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.1620070104
Subject(s) - bessel function , helmholtz equation , mathematics , finite element method , scalar (mathematics) , mathematical analysis , rotational symmetry , helmholtz free energy , cylindrical harmonics , geometry , physics , boundary value problem , orthogonal polynomials , classical orthogonal polynomials , gegenbauer polynomials , quantum mechanics , thermodynamics
A new family of triangular finite elements is described, useful for solving the axisymmetric vector Helmholtz equation, and a variety of scalar Helmholtz equation problems which lead to generalized Bessel equations of some order m . This family is similar in principle to the scalar axisymmetric Helmholtz elements derived earlier, but requires both reformulation of its describing equations and corresponding new universal element matrices, for successful computational implementation. The necessary formulation is given in this paper. Matrix elements to the sixth‐order inclusive have been calculated and extensively tested computationally.