Siriguleng He

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A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple (L (2)(Ω)(2)) space replacing the complex H(div; Ω)(More)
Anovel characteristic expandedmixed finite elementmethod is proposed and analyzed for reaction-convection-diffusion problems. The diffusion term ∇ ⋅ (a(x, t)∇u) is discretized by the novel expanded mixed method, whose gradient belongs to the square integrable space instead of the classical H(div; Ω) space and the hyperbolic part d(x)(∂u/∂t) + c(x, t) ⋅ ∇u(More)
In this paper, the C-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(More)
A new numerical scheme based on the H-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(More)
We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite(More)
We propose and analyze a new numericalmethod, called a couplingmethod based on a new expandedmixed finite element (EMFE) and finite element (FE), for fourth-order partial differential equation of parabolic type. We first reduce the fourth-order parabolic equation to a coupled system of second-order equations and then solve a second-order equation by(More)