Finite elements on the sphere

A Comparison of Popular Point Configurations on $\mathbb{S}^2$

“…In applications involving radial basis functions, "1-bit" sensing, and finite element methods ( [27], [41], [50], and [58]), there is interest in precise bounds on D C (ω N ), δ(ω N ), η(ω N ), and γ(ω N ). A trivial lower bound is γ(ω N ) ≥ 1/2 for any configuration.…”

A Tree Algorithm for Isotropic Finite Elements on the Sphere

“…isotropic finite elements on the sphere has been established. The kernels Γ j , as defined by (23), are known in spectral form as orthogonal expansions in terms of Legendre functions, where the coefficients (L…”

“…We start by repeating some formulas for L (k) h known from the investigations in e.g. [7], [20], [22], [23]. …”

“…Seen from practical point of view, singular integrals with a local support would be the better choice. In this respect one is naturally led to start from the piecewise polynomial function L [5], [7], [9], [23]) of the form…”

Approximation of parabolic PDEs on spheres using spherical basis functions

“…Approximation of partial differential equations on spheres has many applications in physical geodesy, potential theory, oceanography, and meteorology [2,17,18]. Evolution equations on spherical geometry such as shallow water equations have been studied in weather forecasting services [3,23].…”