9 citations · 18 across the 6 of their papers we have counts for
7 papers
A finite element method for Dirichlet boundary control of elliptic partial differential equations
Shaohong Du, Zhiqiang Cai
This paper introduces a new variational formulation for Dirichlet boundary control problem of elliptic partial differential equations, based on observations that the state and adjo…
Robust residual-based a posteriori error estimators for mixed finite element methods for fourth order elliptic singularly perturbed problems
Shaohong Du, Runchang Lin, Zhimin Zhang
We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the erro…
Robust recovery-type a posteriori error estimators for streamline upwind/Petrov Galerkin discretizations for singularly perturbed problems
Shaohong Du, Runchang Lin, Zhimin Zhang
In this paper, we investigate adaptive streamline upwind/Petrov Galerkin (SUPG) methods for singularly perturbed convection-diffusion-reaction equations in a new dual norm presente…
Convergence of adaptive mixed finite element method for convection-diffusion-reaction equations
Shaohong Du, Xiaoping Xie
We prove the convergence of an adaptive mixed finite element method (AMFEM) for (nonsymmetric) convection-diffusion-reaction equations. The convergence result holds from the cases…
Residual-based a posteriori error estimation for multipoint flux mixed finite element methods
Shaohong Du, Shuyu Sun, Xiaoping Xie
A novel residual-type {\it a posteriori} error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimen…
New residual-based a posteriori error estimators for lowest-order Raviart-Thomas element approximation to convection-diffusion-reaction equations
Shaohong Du, Xiaoping Xie
A new technique of residual-type a posteriori error analysis is developed for the lowest-order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction…