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Fully discrete local discontinuous Galerkin method for solving the fractional telegraph equation

This paper aims to develop a fully discrete local discontinuous Galerkin finite element method for numerical simulation of the time-fractional telegraph equation, where the fractional derivative is… Expand

A stabilised characteristic finite element method for transient Navier–Stokes equations

In this work, we consider a stabilised characteristic finite element method for the time-dependent Navier–Stokes equations based on the lowest equal-order finite element pairs. The diffusion term in… Expand

Unconditional stability and error estimates of modified characteristics FEMs for the Navier–Stokes equations

The paper is concerned with the unconditional stability and convergence of characteristics type methods for the time-dependent Navier–Stokes equations. We present optimal error estimates in $$L^2$$L2… Expand

A New Error Analysis of Characteristics-Mixed FEMs for Miscible Displacement in Porous Media

The method of characteristics type is especially effective for convection-dominated diffusion problems. Due to the nature of characteristic temporal discretization, the method allows one to use a… Expand

Modified Characteristics Gauge–Uzawa Finite Element Method for Time Dependent Conduction–Convection Problems

- Z. Si, Xiaogang Song, P. Huang
- Computer Science, Mathematics
- J. Sci. Comput.
- 2014

In this paper, we give the modified characteristics Gauge–Uzawa finite element method (MCGUFEM) for time dependent conduction–convection problems, which is gotten by combining the modified… Expand

A defect-correction method for unsteady conduction convection problems I: spatial discretization

In this paper, a semi-discrete defect-correction mixed finite element method (MFEM) for solving the non-stationary conduction-convection problems in two dimension is presented. In this method, we… Expand

Decoupled two‐grid finite element method for the time‐dependent natural convection problem I: Spatial discretization

- T. Zhang, Jinyun Yuan, Z. Si
- Mathematics
- 1 November 2015

In this article, a decoupled two grid finite element method (FEM) is proposed and analyzed for the nonsteady natural convection problem using the coarse grid numerical solutions to decouple the… Expand

Decoupled modified characteristics finite element method for the time dependent Navier–Stokes/Darcy problem†

- Z. Si, Yunxia Wang, S. Li
- Mathematics
- 25 June 2013

In this paper, a modified characteristics finite element method for the time dependent Navier–Stokes/Darcy problem with the Beavers–Joseph–Saffman interface condition is presented. In this method,… Expand

Second order modified method of characteristics mixed defect-correction finite element method for time dependent Navier–Stokes problems

- Z. Si
- Mathematics, Computer Science
- Numerical Algorithms
- 1 February 2012

In this paper, a second order modified method of characteristics defect-correction (SOMMOCDC) mixed finite element method for the time dependent Navier–Stokes problems is presented. In this method,… Expand

New one- and two-level Newton iterative mixed finite element methods for stationary conduction-convection problems

In this article, new one- and two-level Newton iterative mixed finite element methods (MFEM) for two-dimensional stationary conduction-convection problems are presented. In both of the methods, we… Expand