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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 H2H^2-equivalent norm. Finally, comprehensive numerical experiments are presented to validate the theoretical analysis and demonstrate the efficiency and robustness of the method.

Keywords

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

R2 v1 2026-07-22T07:08:11.624Z