Hongxing Rui

A second order characteristic finite element scheme for convection-diffusion problems

Summary. A new characteristic finite element scheme is presented for It is of second order accuracy in time increment, symmetric, and unconditionally stable. Optimal error estimates are proved in the framework of

A Block-Centered Finite Difference Method for the Darcy--Forchheimer Model

L^2

Mixed Element Method for Two-Dimensional Darcy-Forchheimer Model

-theory. Numerical results are presented for two examples, which show the advantage of the scheme.

A Priori Error Estimates for Optimal Control Problems Governed by Transient Advection-Diffusion Equations

A block-centered finite difference scheme is introduced to solve the nonlinear Darcy--Forchheimer equation, in which the velocity and pressure can be approximated simultaneously. The second-order error estimates for both pressure and velocity are established on a nonuniform rectangular grid. Numerical experiments using the scheme show the consistency of the convergence rates of our method with the theoretical analysis.

A Two-Grid Block-Centered Finite Difference Method For Darcy--Forchheimer Flow in Porous Media

A mixed element method is introduced to solve Darcy-Forchheimer equation, in which the velocity and pressure are approximated by mixed element such as Raviart-Thomas, Brezzi-Douglas-Marini element. We establish the existence and uniqueness of the problem. Error estimates are presented based on the monotonicity owned by the Forchheimer term. An iterative scheme is given for practical computation. The numerical experiments using the lowest order Raviart-Thomas (RT0) mixed element show that the convergence rates of our method are in agree with the theoretical analysis.

A Mass-Conservative Characteristic Finite Element Scheme for Convection-Diffusion Problems

AbstractIn this paper, we investigate a characteristic finite element approximation of quadratic optimal control problems governed by linear advection-dominated diffusion equations, where the state and co-state variables are discretized by piecewise linear continuous functions and the control variable is approximated by piecewise constant functions. We derive some a priori error estimates for both the control and state approximations. It is proved that these approximations have convergence order

Symmetric modified finite volume element methods for self-adjoint elliptic and parabolic problems

\mathcal{O}(h_{U}+h+k)

Characteristic block-centred finite difference methods for nonlinear convection-dominated diffusion equation

, where hU and h are the spatial mesh-sizes for the control and state discretization, respectively, and k is the time increment. Numerical experiments are presented, which verify the theoretical results.

A two-grid block-centered finite difference method for nonlinear non-Fickian flow model

A two-grid block-centered finite difference method is proposed for solving the two-dimensional Darcy--Forchheimer model describing non-Darcy flow in porous media. To construct the two-grid method we modify the original nonlinear elliptic operator of Darcy--Forchheimer flow to a twice continuously differentiable one by introducing a small and positive parameter

A characteristic-mixed finite element method for time-dependent convection–diffusion optimal control problem

\varepsilon