2 citations · 3 across the 6 of their papers we have counts for
6 papers
Superconvergent quadriatic finite element on uniform tetrahedral meshes
Yunqing Huang, Shangyou Zhang
By a direct computation, we show that the interpolation of a function is also a local -projection on uniform tetrahedral meshes, i.e., the difference is -orth…
Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features
Ke Li, Yaqin Zhang, Yunqing Huang +2
This paper proposes an Adaptive Basis-inspired Deep Neural Network (ABI-DNN) for solving partial differential equations with localized phenomena such as sharp gradients and singula…
A posteriori error estimators for fourth order elliptic problems with concentrated loads
Huihui Cao, Yunqing Huang, Nianyu Yi +1
In this paper, we study two residual-based a posteriori error estimators for the interior penalty method in solving the biharmonic equation in a polygonal domain under a conc…
Multicontinuum homogenization in perforated domains
Wei Xie, Yalchin Efendiev, Yunqing Huang +2
In this paper, we develop a general framework for multicontinuum homogenization in perforated domains. The simulations of problems in perforated domains are expensive and, in many…
Recovery type a posteriori error estimation of an adaptive finite element method for Cahn--Hilliard equation
Yaoyao Chen, Yunqing Huang, Nianyu Yi +1
In this paper, we derive a novel recovery type a posteriori error estimation of the Crank-Nicolson finite element method for the Cahn--Hilliard equation. To achieve this, we employ…
Error Analysis of Physics-Informed Neural Networks for Approximating Dynamic PDEs of Second Order in Time
Yanxia Qian, Yongchao Zhang, Yunqing Huang +1
We consider the approximation of a class of dynamic partial differential equations (PDE) of second order in time by the physics-informed neural network (PINN) approach, and provide…