7 papers
A stabilized nonconforming finite element method for the surface biharmonic problem
Shuonan Wu, Hao Zhou
This paper presents a novel stabilized nonconforming finite element method for solving the surface biharmonic problem. The method extends the New-Zienkiewicz-type (NZT) element to…
Exponentially-fitted finite elements for and convection-diffusion problems
Jindong Wang, Shuonan Wu
This paper presents a novel approach to the construction of the lowest order and exponentially-fitted finite element spaces ${\mathcal{S}_{1^-}…
A Monotone Discretization for the Fractional Obstacle Problem
Rubing Han, Shuonan Wu, Hao Zhou
We introduce a novel monotone discretization method for addressing obstacle problems involving the integral fractional Laplacian with homogeneous Dirichlet boundary conditions over…
A hybridizable discontinuous Galerkin method for magnetic advection-diffusion problems
Jindong Wang, Shuonan Wu
We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for solving a mixed magnetic advection-diffusion problem within a more general Friedrichs system framework…
Two families of -rectangle nonconforming finite elements for sixth-order elliptic equations
Xianlin Jin, Shuonan Wu
In this paper, we propose two families of nonconforming finite elements on -rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent propert…
Discontinuous Galerkin methods for magnetic advection-diffusion problems
Jindong Wang, Shuonan Wu
We devise and analyze a class of the primal discontinuous Galerkin methods for the magnetic advection-diffusion problems based on the weighted-residual approach. In addition to the…