A Least-Squares Weak Galerkin Method for Second-Order Elliptic Equations in Non-Divergence Form
Numerical Analysis
2026-05-13 v1 Numerical Analysis
Abstract
This article proposes a novel least-squares weak Galerkin (LS-WG) method for second-order elliptic equations in non-divergence form. The approach leverages a locally defined discrete weak Hessian operator constructed within the weak Galerkin framework. A key feature of the resulting algorithm is that it yields a symmetric and positive definite linear system while remaining applicable to general polygonal and polyhedral meshes. We establish optimal-order error estimates for the approximation in a discrete -equivalent norm. Finally, comprehensive numerical experiments are presented to validate the theoretical analysis and demonstrate the efficiency and robustness of the method.
Cite
@article{arxiv.2605.12417,
title = {A Least-Squares Weak Galerkin Method for Second-Order Elliptic Equations in Non-Divergence Form},
author = {Chunmei Wang and Shangyou Zhang},
journal= {arXiv preprint arXiv:2605.12417},
year = {2026}
}
Comments
18 pages, 8 tables, 2 figures