Excellence in Research and Innovation for Humanity

Yang Liu

Publications

7

Publications

7
912
A C1-Conforming Finite Element Method for Nonlinear Fourth-Order Hyperbolic Equation
Abstract:

In this paper, the C1-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes.

Keywords:
Nonlinear fourth-order hyperbolic equation, Lyapunov functional, existence, uniqueness and regularity, conforming finite element method, optimal error estimates.
6
2281
An H1-Galerkin Mixed Method for the Coupled Burgers Equation
Abstract:

In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.

Keywords:
The coupled Burgers equation, H1-Galerkin mixed finite element method, Backward Euler's method, Optimal error estimates.
5
9513
A New Time Discontinuous Expanded Mixed Element Method for Convection-dominated Diffusion Equation
Abstract:

In this paper, a new time discontinuous expanded mixed finite element method is proposed and analyzed for two-order convection-dominated diffusion problem. The proofs of the stability of the proposed scheme and the uniqueness of the discrete solution are given. Moreover, the error estimates of the scalar unknown, its gradient and its flux in the L1( ¯ J,L2( )-norm are obtained.

Keywords:
Convection-dominated diffusion equation, expanded mixed method, time discontinuous scheme, stability, error estimates.
4
9984
A New Splitting H1-Galerkin Mixed Method for Pseudo-hyperbolic Equations
Abstract:

A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

Keywords:
Pseudo-hyperbolic equations, splitting system, H1-Galerkin mixed method, error estimates.
3
10420
A Nonconforming Mixed Finite Element Method for Semilinear Pseudo-Hyperbolic Partial Integro-Differential Equations
Abstract:

In this paper, a nonconforming mixed finite element method is studied for semilinear pseudo-hyperbolic partial integrodifferential equations. By use of the interpolation technique instead of the generalized elliptic projection, the optimal error estimates of the corresponding unknown function are given.

Keywords:
Pseudo-hyperbolic partial integro-differential equations, Nonconforming mixed element method, Semilinear, Error estimates.
2
12587
An Adaptive Least-squares Mixed Finite Element Method for Pseudo-parabolic Integro-differential Equations
Abstract:

In this article, an adaptive least-squares mixed finite element method is studied for pseudo-parabolic integro-differential equations. The solutions of least-squares mixed weak formulation and mixed finite element are proved. A posteriori error estimator is constructed based on the least-squares functional and the posteriori errors are obtained.

Keywords:
Pseudo-parabolic integro-differential equation, least squares mixed finite element method, adaptive method, a posteriori error estimates.
1
16825
A New Approximate Procedure Based On He’s Variational Iteration Method for Solving Nonlinear Hyperbolic Wave Equations
Abstract:

In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.

Keywords:
Hyperbolic wave equation, Nonlinear, He’s variational iteration method, Transformations