We apply in this paper the weak Galerkin method to the second order parabolic differential equations based on a discrete weak gradient operator. We establish both the continuous time and the discrete time weak Galerkin finite element schemes, which allow using the totally discrete functions in approximation space and the finite element partitions of arbitrary polygons with certain shape regular...

We present a library for the computation of the shape functions for the element free Galerkin (EFG) method. While the EFG method is in many respects strikingly similar to the finite element method, the construction of the shape functions for the EFG method is much more complicated than in the FEM. Thus, the question arises whether it is possible to encapsulate the complexity of the shape functi...

Abstract. A C0-weak Galerkin (WG) method is introduced and analyzed for solving the biharmonic equation in 2D and 3D. A weak Laplacian is defined for C0 functions in the new weak formulation. This WG finite element formulation is symmetric, positive definite and parameter free. Optimal order error estimates are established in both a discrete H2 norm and the L2 norm, for the weak Galerkin finite...

Discontinuous Galerkin (DG) and matrix-free finite element methods with a novel projective pressure estimation are combined to enable the numerical modeling of magma dynamics in 2D and 3D using the library deal.II . The physical model is an advection-reaction type system consisting of two hyperbolic equations to evolve porosity and soluble mineral abundance and one elliptic equation to recover ...

The meshless element-free Galerkin method (EFGM) is used to solve partial differential equations responsible for obtaining the electromagnetic fields generated by a transmission line. For this purpose, 2D model based in real line constructed and simulated. results obtained EFGM have good accuracy they are compared against analytical solution Finite Element Method order verify effectiveness, adv...

We propose and analyze a finite element method for a semi– stationary Stokes system modeling compressible fluid flow subject to a Navier– slip boundary condition. The velocity (momentum) equation is approximated by a mixed finite element method using the lowest order Nédélec spaces of the first kind. The continuity equation is approximated by a standard piecewise constant upwind discontinuous G...