22 citations · 38 across the 3 of their papers we have counts for
3 papers
math.NA2021★ 10 cited
A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems
Yu Leng, Xiaochuan Tian, Leszek Demkowicz +2
We present a Petrov-Gelerkin (PG) method for a class of nonlocal convection-dominated diffusion problems. There are two main ingredients in our approach. First, we define the norm…
math.NA2020★ 22 cited
Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation
Yu Leng, Xiaochuan Tian, Nathaniel A. Trask +1
In this work, we study the reproducing kernel (RK) collocation method for the peridynamic Navier equation. We first apply a linear RK approximation on both displacements and dilata…
math.NA2019★ 6 cited
Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion
Yu Leng, Xiaochuan Tian, Nathaniel Trask +1
Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation…