A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic
equation formulated as a system of two first order linear equations. This method, called WG …

In the present paper we introduce a Virtual Element Method (VEM) for the approximate
solution of general linear second order elliptic problems in mixed form, allowing for variable …

This paper introduces a new weak Galerkin (WG) finite element method for second order
elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a …

A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper
for solving second order elliptic equations with discontinuous coefficients and interfaces …

Increased attention has been paid on numerical modeling of interface problems as its wide
applications in various aspects of science. Motivated by enhancing the application of the …

In this paper, we propose a novel mesh-free numerical method for solving the elliptic
interface problems based on deep learning. We approximate the solution by the neural …

This article is assigned to the numerical analysis of a new weak Galerkin mixed-type finite
element method for the diffusion-convection-reaction problem with singular perturbation …

In recent years, there have been extensive efforts to find the numerical methods for solving
problems with interface. The main idea of this work is to introduce an efficient truly meshless …

Abstract The Cahn-Hilliard phase-field model of two-phase incompressible flows, namely
the Cahn-Hilliard-Navier-Stokes (CH-NS) problem represents the fundamental building …

In this work, we propose an efficient meshfree method based on Pascal polynomials and
multiple-scale approach for numerical solutions of two-dimensional (2-D) and three …