Year: 2026
Type: article
Abstract: In this paper, we develop an efficient Fourier-Legendre spectral-Galerkin method for solving elliptic partial differential equations on general two-dimensional domains. A key core of our approach is employing a harmonic map to handle the general physical domains. This technique ensures broad geometric applicability, making the method highly effective for both complex star-shaped and nonstar-shaped domains. Moreover, this method is rigorously proved, with optimal convergence results established under $$H^1$$ H 1 -norm, which is independent of the domain boundary’s smoothness. The effectiveness and generality of the scheme are validated through some numerical examples on a wide variety of complex geometries.
Source: Journal of Scientific Computing
Authors: Shan Shi, Xiaoyun Jiang, Fanhai Zeng, Hui Zhang
Institutions: Shandong University, Hong Kong Polytechnic University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7143329982