16 citations · 33 across the 16 of their papers we have counts for
4 papers · 1 filter
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…
Battling Gibbs Phenomenon: On Finite Element Approximations of Discontinuous Solutions of PDEs
Shun Zhang
In this paper, we want to clarify the Gibbs phenomenon when continuous and discontinuous finite elements are used to approximate discontinuous or nearly discontinuous PDE solutions…
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…
Robust and Local Optimal A Priori Error Estimates for Interface Problems with Low Regularity: Mixed Finite Element Approximations
Shun Zhang
For elliptic interface problems in two- and three-dimensions with a possible very low regularity, this paper establishes a priori error estimates for the Raviart-Thomas and Brezzi-…