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- QIAN LI, WANFANG SHEN, JINFENG JIAN
- 2005

We consider finite element methods applied to a class of quasi para-bolic integro-differential equations in R d. Global strong superconvergence, which only requires that partitions are quasi-uniform, is investigated for the error between the approximate solution and the Sobolev-Volterra projection of the exact solution. Two order superconvergence results… (More)

- Guoliang Yang, Wanfang Shen, Daqun Zhang, Wenbin Liu
- JORS
- 2014

In this paper, we discuss the relationship between multi-attribute utility theory and DEA models without explicit inputs (DEA-WEI), including dual models and some theoretical analysis of DEA-WEI models. We then propose generic DEA-WEI models with quadratic utility terms. Finally, we provide illustrative examples to show that DEA-WEI with suitable quadratic… (More)

- WANFANG SHEN, LIANG GE, DANPING YANG, X. Cui
- 2013

In this paper, the mathematical formulation for a quadratic optimal control problem governed by a linear quasi-parabolic integro-differential equation is studied, the optimality conditions are derived, and then the a priori error estimate for its finite element approximation is given. Furthermore some numerical tests are performed to verify the theoretical… (More)

- Wanfang Shen, Hua Su, Xinguang Zhang
- 2014

and Applied Analysis 3 We are interested in the following optimal control problem: min u∈Uad⊂X J ( u, y u ) 1 2 {∫T 0 ∥ ∥y − zd ∥ ∥2 0,Ωdt ∫T 0 ‖u‖0,ΩUdt } , 2.1 subject to yt − div ( A∇yt D∇y ∫ t 0 C t, τ ∇y x, τ dτ ) f Bu, in Ω × 0, T , y 0, on ∂Ω × 0, T , y|t 0 y0, in Ω, 2.2 where u is control, y is state, zd is the observation, Uad is a closed convex… (More)

- Wanfang Shen, Liang Ge, Danping Yang, Wenbin Liu
- J. Sci. Comput.
- 2015

- Wanfang Shen, Daqun Zhang, Wenbin Liu, Guoliang Yang
- Computers & OR
- 2016

- Tongjun Sun, Wanfang Shen, Benxue Gong, Wenbin Liu
- J. Sci. Comput.
- 2016

- Wanfang Shen
- 2011 Fourth International Conference on…
- 2011

We consider finite element methods applied to a class of quasi-hyperbolic integro-differential equations. Global strong super convergence, which only requires that partitions are quasi-uniform, is investigated for the error between the approximate solution and the Sobolev-Volterra projection of the exact solution. We employ a special method for initial… (More)

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