A stabilizer free weak Galerkin (WG) finite element method on polytopal mesh has been introduced in Part I of this paper (Ye and Zhang (2020)). Removing stabilizers from discontinuous methods simplifies formulations reduces programming complexity. The purpose is to introduce a new WG without that convergence rates one order higher than optimal rates. This the first achieves superconvergence mes...

A weak Galerkin (WG) finite element method without stabilizers was introduced in Ye and Zhang (2020) on polytopal mesh. Then it improved (2021) with order one superconvergence. The goal of this paper is to develop a new stabilizer free WG This has convergence rates two orders higher than the optimal for corresponding solution both an energy norm L2 norm. numerical examples are tested low high e...

A scheme using the mesh-free generalized finite differencing (GFD) on flows past moving bodies is proposed. The aim is to devise a method to simulate flow past an immersed moving body that avoids the intensive remeshing of the computational domain and minimizes data interpolation associated with the established computational fluid methodologies; as such procedures are time consuming and are a s...

Difficulties associated with free-surface finite element flow simulations are related to a) nonlinear and advective nature of most hydrodynamic flows, b) requirements for compatibility between velocity and pressure interpolation, c) maintaining a valid computational mesh in the presence of moving boundaries, and d) enforcement of the kinematic conditions at the free surface. Focusing on the las...

High-quality meshes are essential in the solution of partial differential equations (PDEs), which arise in numerous science and engineering applications, as the mesh quality affects the solution accuracy, the solver execution time, and the problem conditioning. Mesh quality improvement is necessary when the mesh is of less than desirable quality (either from mesh generation or deformation). Non...

The main aim of this paper is to investigate bending behavior in sandwich plates with functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets with considering the effects of carbon nanotube (CNT) aggregation. The sandwich plates are assumed resting on Winkler-Pasternak elastic foundation and a mesh-free method based on first order shear deformation theory (FSDT) is devel...