A Low Order Globally Divergence-Free WG Finite Element Method for Steady Thermally Coupled Incompressible MHD Flow

Robust globally divergence-free Weak Galerkin finite element method for incompressible Magnetohydrodynamics flow

A new weak Galerkin finite element method for elliptic interface problems

A weak Galerkin finite element scheme with boundary continuity for second-order elliptic problems

A stabilizer-free weak Galerkin finite element method on polytopal meshes

An efficient numerical scheme for the biharmonic equation by weak Galerkin finite element methods on polygonal or polyhedral meshes

Weak Galerkin finite element methods for quad-curl problems

A weak Galerkin finite element method for 1D semiconductor device simulation models

This article establishes a discrete maximum principle (DMP) for the approximate solution of convection–diffusion–reaction problems obtained from the weak Galerkin (WG) finite element method on nonuniform rectangular partitions. The DMP analysis is based on a simplified formulation of the WG involving only the approximating functions defined on the boundary of each element. The simplified weak Galerkin (SWG) method has a reduced computational complexity over the usual WG, and indeed provides a discretization scheme different from the WG when the reaction terms are present. An application of the SWG on uniform rectangular partitions yields some 5‐ and 7‐point finite difference schemes for the second order elliptic equation. Numerical experiments are presented to verify the DMP and the accuracy of the scheme, particularly the finite difference scheme.

A modified weak Galerkin finite element method for the linear elasticity problem in mixed form

A weak Galerkin finite element method for second-order elliptic problems

A modified weak Galerkin finite element method for the Stokes equations

This paper proposes and analyzes a weak Galerkin (WG) finite element method with strong symmetric stresses for two- and three-dimensional linear elasticity problems on conforming or nonconforming polygon/polyhedral meshes. The WG method uses piecewise-polynomial approximations of degrees k ( ≥ 1 ${\geq 1}$ ) for the stress, k + 1 ${k+1}$ for the displacement, and k for the displacement trace on the inter-element boundaries. It is shown to be equivalent to a hybridizable discontinuous Galerkin (HDG) finite element scheme. We show that the WG methods are robust in the sense that the derived a priori error estimates are optimal and uniform with respect to the Lamé constant λ. Numerical experiments confirm the theoretical results.

The energy-diminishing weak Galerkin finite element method for the computation of ground state and excited states in Bose-Einstein condensates

A weak Galerkin finite element method for nonlinear convection-diffusion equation

A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation