A nine point scheme is presented for discretizing diffusion operators on distorted
quadrilateral meshes. The advantage of this method is that highly distorted meshes can be …

In this paper, the discontinuous finite volume element method (DFVEM) is considered to
solve the Allen-Cahn equation which contains strong nonlinearity. The method is based on …

We establish a general framework for analyzing the class of finite volume methods which
employ continuous or totally discontinuous trial functions and piecewise constant test …

In this paper, we report our recent advances on vertex centered finite volume element
methods (FVEMs) for second order partial differential equations (PDEs). We begin with a …

We develop a new discontinuous finite volume method for solving the Stokes equations on
both triangular and rectangular meshes. An optimal error estimate for the approximation of …

In this paper, we propose a discontinuous finite volume element method to solve a phase
field model for two immiscible incompressible fluids. In this finite volume element scheme …

The sedimentation–consolidation and flow processes of a mixture of small particles
dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear …

We establish a general framework for analyzing the class of finite volume methods for the
Stokes equations. Under the framework, optimal order convergence for velocity and …

In this paper, a discontinuous finite volume element method was presented to solve the
nonstationary Stokes–Darcy problem for the coupling fluid flow in conduits with porous …

The incompressible miscible displacement problem in porous media is modeled by a
coupled system of two nonlinear partial differential equations, the pressure‐velocity …