34 citations · 92 across the 23 of their papers we have counts for
25 papers
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…
A finite element approximation of planar oblique derivative problems in non-divergence form
Guangwei Gao, Shuonan Wu
This paper proposes a (non-Lagrange) primal finite element approximation of the linear elliptic equations in non-divergence form with oblique boundary conditions in planar,…
A monotone discretization for integral fractional Laplacian on bounded Lipschitz domains: Pointwise error estimates under Hölder regularity
Rubing Han, Shuonan Wu
We propose a monotone discretization for the integral fractional Laplace equation on bounded Lipschitz domains with the homogeneous Dirichlet boundary condition. The method is insp…
Finite Element Approximations of a Class of Nonlinear Stochastic Wave Equation with Multiplicative Noise
Yukun Li, Shuonan Wu, Yulong Xing
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the medi…
Robust BPX Preconditioner for Fractional Laplacians on Bounded Lipschitz Domains
Juan Pablo Borthagaray, Ricardo H. Nochetto, Shuonan Wu +1
We propose and analyze a robust BPX preconditioner for the integral fractional Laplacian on bounded Lipschitz domains. For either quasi-uniform grids or graded bisection grids, we…
A parallel-in-time algorithm for high-order BDF methods for diffusion and subdiffusion equations
Shuonan Wu, Zhi Zhou
In this paper, we propose a parallel-in-time algorithm for approximately solving parabolic equations. In particular, we apply the -step backward differentiation formula, and the…
On the unisolvence for the quasi-polynomial spaces of differential forms
Shuonan Wu, Ludmil T. Zikatanov
We consider quasi-polynomial spaces of differential forms defined as weighted (with a positive weight) spaces of differential forms with polynomial coefficients. We show that the u…
finite element approximations of linear elliptic equations in non-divergence form and Hamilton-Jacobi-Bellman equations with Cordes coefficients
Shuonan Wu
This paper is concerned with (non-Lagrange) finite element approximations of the linear elliptic equations in non-divergence form and the Hamilton-Jacobi-Bellman (HJB) equati…
An Extended Galerkin Analysis for Elliptic Problems
Qingguo Hong, Shuonan Wu, Jinchao Xu
A general analysis framework is presented in this paper for many different types of finite element methods (including various discontinuous Galerkin methods). For second order elli…
A mixed discontinuous Galerkin method with symmetric stress for Brinkman problem based on the velocity-pseudostress formulation
Yanxia Qian, Shuonan Wu, Fei Wang
The Brinkman equations can be regarded as a combination of the Stokes and Darcy equations which model transitions between the fast flow in channels (governed by Stokes equations) a…
A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry
Fei Wang, Shuonan Wu, Jinchao Xu
In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in -dimension ($d…
Simplex-averaged finite element methods for , and convection-diffusion problems
Shuonan Wu, Jinchao Xu
This paper is devoted to the construction and analysis of the finite element approximations for the convection-diffusion problems, where can be chosen as , $…
Analysis of the Morley element for the Cahn-Hilliard equation and the Hele-Shaw flow
Shuonan Wu, Yukun Li
The paper analyzes the Morley element method for the Cahn-Hilliard equation. The objective is to derive the optimal error estimates and to prove the zero-level sets of the Cahn-Hil…
A Unified Study of Continuous and Discontinuous Galerkin Methods
Qingguo Hong, Fei Wang, Shuonan Wu +1
A unified study is presented in this paper for the design and analysis of different finite element methods (FEMs), including conforming and nonconforming FEMs, mixed FEMs, hybrid F…
Interior Penalty Nonconforming Finite Element Methods for -th Order PDEs in
Shuonan Wu, Jinchao Xu
In general -dimensional simplicial meshes, we propose a family of interior penalty nonconforming finite element methods for -th order partial differential equations, where $…
Nonconforming Finite Element Spaces for -th Order Partial Differential Equations on Simplicial Grids When
Shuonan Wu, Jinchao Xu
In this paper, we propose a family of nonconforming finite elements for -th order partial differential equations in on simplicial grids when . This family…
New Hybridized Mixed Methods for Linear Elasticity and Optimal Multilevel Solvers
Shihua Gong, Shuonan Wu, Jinchao Xu
In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions , which yields a conforming and strongly symmetric a…
On the Stability and Accuracy of Partially and Fully Implicit Schemes for Phase Field Modeling
Jinchao Xu, Yukun Li, Shuonan Wu +1
We study in this paper the accuracy and stability of partially and fully implicit schemes for phase field modeling. Through theoretical and numerical analysis of Allen-Cahn and Cah…
Multiphase Allen-Cahn and Cahn-Hilliard Models and Their Discretizations with the Effect of Pairwise Surface Tensions
Shuonan Wu, Jinchao Xu
In this paper, the mathematical properties and numerical discretizations of multiphase models that simulate the phase separation of an -component mixture are studied. For the ge…
A Second Order Time Homogenized Model for Sediment Transport
Yuchen Jiang, Ruo Li, Shuonan Wu
A multi-scale method for the hyperbolic systems governing sediment transport in subcritical case is developed. The scale separation of this problem is due to the fact that the sedi…