Dispersion Characteristics and Applications of Higher Order Isosceles Triangular Meshes in the Finite Element Method

Mesh division plays an important role in applications of the finite element method (FEM). The proposed research shows that under the same order, the equilateral triangular meshes have the most uniform dispersion distribution. The isosceles triangles with equal base and height have more uniform dispersion error than the square meshes, while the maximum phase error is similar. Taking the rectangular waveguide as an example, the relative errors in the cut-off frequency are analyzed based on different meshes. The numerical results show that under the same interpolation order and node numbers, the relative error of isosceles triangles with equal base and height for TE10 mode is the smallest. The results are useful in choosing appropriate element order, node density and mesh shape when applying FEM.