Galerkin approximation for elliptic PDEs on spheres |
| |
Authors: | QT Le Gia |
| |
Institution: | Department of Mathematics, College Station, Texas A&M University, TX 77843-3368, USA |
| |
Abstract: | We discuss a Galerkin approximation scheme for the elliptic partial differential equation -Δu+ω2u=f on SnRn+1. Here Δ is the Laplace–Beltrami operator on Sn, ω is a non-zero constant and f belongs to C2k-2(Sn), where kn/4+1, k is an integer. The shifts of a spherical basis function φ with φHτ(Sn) and τ>2kn/2+2 are used to construct an approximate solution. An H1(Sn)-error estimate is derived under the assumption that the exact solution u belongs to C2k(Sn). |
| |
Keywords: | Spherical basis function Galerkin method |
本文献已被 ScienceDirect 等数据库收录! |
|