Triangular finite elements for the generalized Bessel equation of order <i>m</i>

Abstract

Abstract 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.