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- 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)

- QIAN LI, WANFANG SHEN, JINFENG JIAN
- 2005

We consider finite element methods applied to a class of quasi parabolic integro-differential equations in R. 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 are… (More)

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

Linear quasi-parabolic integro-differential equations and their control appear in many scientific problems and engineering applications such as biology mechanics, nuclear reaction dynamics, heat conduction in materials with memory, and visco-elasticity, etc.. The existence and uniqueness of the solution of the linear quasi-parabolic integro-differential… (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
- 2014

We extend the existing techniques to study semidiscrete adaptive finite element approximation schemes for a constrained optimal control problem governed by parabolic integrodifferential equations. The control problem involves time accumulation and the control constrain is given in an integral obstacle sense. We first prove the uniqueness and existence of… (More)

- 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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