56 citations · 368 across the 53 of their papers we have counts for
53 papers
Edge-averaged virtual element methods for convection-diffusion and convection-dominated problems
Shuhao Cao, Long Chen, Seulip Lee
This manuscript develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a…
A New Div-Div-Conforming Symmetric Tensor Finite Element Space with Applications to the Biharmonic Equation
Long Chen, Xuehai Huang
A new -conforming finite element is presented, which avoids the need for super-smoothness by redistributing the degrees of freedom to edges and faces. This lead…
Accelerated Gradient and Skew-Symmetric Splitting Methods for a Class of Monotone Operator Equations
Long Chen, Jingrong Wei
A class of monotone operator equations, which can be decomposed into sum of the gradient of a strongly convex function and a linear and skew-symmetric operator, is considered in th…
Complexes from Complexes: Finite Element Complexes in Three Dimensions
Long Chen, Xuehai Huang
In the field of solving partial differential equations (PDEs), Hilbert complexes have become highly significant. Recent advances focus on creating new complexes using the Bernstein…
Transformed Primal-Dual Methods For Nonlinear Saddle Point Systems
Long Chen, Jingrong Wei
A transformed primal-dual (TPD) flow is developed for a class of nonlinear smooth saddle point system. The flow for the dual variable contains a Schur complement which is strongly…
Finite Element de Rham and Stokes Complexes in Three Dimensions
Long Chen, Xuehai Huang
Finite element de Rham complexes and finite element Stokes complexes with various smoothness in three dimensions are systematically constructed. First smooth scalar finite elements…