Fourier-Galerkin algorithm for 2D localized solutions

Abstract

The paper presents the numerical implementation in 2D of Fourier-Galerkin expansion with complete orthonormal basis system of localized functions. The bilinear Laplace equation is considered as a featuring example. Coordinate splitting is used to reduce the cost of inversion of the linear matrices for the coefficients. The axisymmetric solution is calculated as a 2D problem and compared to a numerical solution, found by means of a difference scheme.