7 citations · 10 across the 4 of their papers we have counts for
6 papers
Least-Squares Methods with Nonconforming Finite Elements for General Second-Order Elliptic Equations
Yuxiang Liang, Shun Zhang
In this paper, we study least-squares finite element methods (LSFEM) for general second-order elliptic equations with nonconforming finite element approximations. The equation may…
Generalized Prager-Synge Inequality and Equilibrated Error Estimators for Discontinuous Elements
Cuiyu He, Zhiqiang Cai, Shun Zhang
The well-known Prager-Synge identity is valid in and serves as a foundation for developing equilibrated a posteriori error estimators for continuous elements. In this pape…
Adaptive Flux-Only Least-Squares Finite Element Methods for Linear Transport Equations
Qunjie Liu, Shun Zhang
In this paper, two flux-only least-squares finite element methods (LSFEM) for the linear hyperbolic transport problem are developed. The transport equation often has discontinuous…
Adaptive First-Order System Least-Squares Finite Element Methods for Second Order Elliptic Equations in Non-Divergence Form
Weifeng Qiu, Shun Zhang
This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical f…
Primal-Dual Reduced Basis Methods for Convex Minimization Variational Problems: Robust True Solution A Posteriori Error Certification and Adaptive Greedy Algorithms
Shun Zhang
In this paper, with the parametric symmetric coercive elliptic boundary value problem as an example of the primal-dual variational problems satisfying the strong duality, we develo…
Adaptive Least-Squares Finite Element Methods for Linear Transport Equations Based on an H(div) Flux Reformulation
Qunjie Liu, Shun Zhang
In this paper, we study the least-squares finite element methods (LSFEM) for the linear hyperbolic transport equations. The linear transport equation naturally allows discontinuous…