Shangyou Zhang

This paper develops and analyzes a least-squares weak Galerkin (LS-WG) finite element method for linear elasticity. By employing weak differential operators, specifically the weak gradient, weak strain tensor, and weak divergence, defined on weak finite element spaces, the proposed framework facilitates the treatment of complex boundary conditions and internal interfaces while avoiding the restrictive discrete inf-sup condition.

We present a least-squares weak Galerkin (LS-WG) finite element method for solving the Stokes equations on arbitrary polygonal and polyhedral meshes. By utilizing discrete weak derivatives on discontinuous polynomial spaces, the proposed framework naturally accommodates complex domain geometries and general partitions.

C.Wang and S.Zhang, “A Simple Weak Galerkin Method for the Brinkman Equations on Nonconvex Polytopal Meshes,” Numerical Methods for Partial Differential Equations42, no. 3 (2026): e70098, https://doi.org/10.1002/num.70098. Conflicts of Interest The authors declare no conflicts of interest. Data Availability Statement No new data were generated or analyzed in this study.