31 citations · 93 across the 12 of their papers we have counts for
11 papers · 1 filter
The Monge-Ampère equation
Michael Neilan, Abner J. Salgado, Wujun Zhang
We review recent advances in the numerical analysis of the Monge-Ampère equation. Various computational techniques are discussed including wide-stencil finite difference schemes, t…
Rates of convergence in -norm for the Monge-Ampère equation
Michael Neilan, Wujun Zhang
We develop discrete -norm error estimates for the Oliker-Prussner method applied to the Monge-Ampère equation. This is obtained by extending discrete Alexandroff estimates a…
The Ericksen Model of Liquid Crystals with Colloidal and Electric Effects
Ricardo H. Nochetto, Shawn W. Walker, Wujun Zhang
We present a robust discretization of the Ericksen model of liquid crystals with variable degree of orientation coupled with colloidal effects and electric fields. The total energy…
Two-scale method for the Monge-Ampère Equation: Pointwise Error Estimates
Ricardo H. Nochetto, Dimitrios Ntogkas, Wujun Zhang
In this paper we continue the analysis of the two-scale method for the Monge-Ampère equation for dimension introduced in [10]. We prove continuous dependence of discrete…
Two-Scale Method for the Monge-Ampère Equation: Convergence to the Viscosity Solution
Ricardo H. Nochetto, Dimitrios Ntogkas, Wujun Zhang
We propose a two-scale finite element method for the Monge-Ampère equation with Dirichlet boundary condition in dimension and prove that it converges to the viscosity solut…
Pointwise rates of convergence for the Oliker-Prussner method for the Monge-Ampère equation
Ricardo H. Nochetto, Wujun Zhang
We study the Oliker-Prussner method exploiting its geometric nature. We derive discrete stability and continuous dependence estimates in the max-norm by using a discrete Alexandrof…
Numerical analysis of strongly nonlinear PDEs
Michael Neilan, Abner J. Salgado, Wujun Zhang
We review the construction and analysis of numerical methods for strongly nonlinear PDEs, with an emphasis on convex and nonconvex fully nonlinear equations and the convergence to…
A finite element method for nematic liquid crystals with variable degree of orientation
Ricardo H. Nochetto, Shawn W. Walker, Wujun Zhang
We consider the simplest one-constant model, put forward by J. Ericksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a di…
Finite element approximation of the Isaacs equation
Abner J. Salgado, Wujun Zhang
We propose and analyze a two-scale finite element method for the Isaacs equation. The fine scale is given by the mesh size whereas the coarse scale is dictated by…
Discrete ABP Estimate and Convergence Rates for Linear Elliptic Equations in Non-divergence Form
Ricardo H. Nochetto, Wujun Zhang
We design a two-scale finite element method (FEM) for linear elliptic PDEs in non-divergence form in a bounded but not necessarily convex domain and st…
An analysis of HDG methods for convection dominated diffusion problems
Guosheng Fu, Weifeng Qiu, Wujun Zhang
In this paper, we establish an a priori error analysis of HDG methods with two types of stabilization parameter applied to convection dominated diffusion problem. We show that, usi…