137 citations · 235 across the 26 of their papers we have counts for
23 papers · 1 filter
The Scott-Vogelius element is inf-sup stable on Freudenthal meshes for
Siqi Ding, Pingbing Ming, Haijun Yu +1
The Scott-Vogelius element is a classical divergence-free mixed finite element for the Stokes problem that has attracted decades of research attention, yet its theoretical framewor…
Spectral Convergence of Random Feature Method in Multiple Dimensions
Pingbing Ming, Hao Yu
We first prove spectral convergence of the random feature method (RFM) for multidimensional targets in Sobolev, Gevrey, ultra-analytic, and bandlimited classes. The analysis establ…
Spectral convergence of random feature method in one dimension
Pingbing Ming, Hao Yu
We first prove the spectral convergence of the random feature method (RFM) when used to solve second-order elliptic equations and eigenvalue problems in one dimension, provided tha…
Generalization Error Estimates of Machine Learning Methods for Solving High Dimensional Schrödinger Eigenvalue Problems
Hao Yu, Yixiao Guo, Pingbing Ming
We propose a machine learning method for computing eigenvalues and eigenfunctions of the Schrödinger operator on a -dimensional hypercube with Dirichlet boundary conditions. The…
Spectral Barron space for deep neural network approximation
Yulei Liao, Pingbing Ming
We prove the sharp embedding between the spectral Barron space and the Besov space with embedding constants independent of the input dimension. Given the spectral Barron space as t…
A Deep Learning Method for Computing Eigenvalues of the Fractional Schrödinger Operator
Yixiao Guo, Pingbing Ming
We present a novel deep learning method for computing eigenvalues of the fractional Schrödinger operator. Our approach combines a newly developed loss function with an innovative n…
A pre-training deep learning method for simulating the large bending deformation of bilayer plates
Xiang Li, Yulei Liao, Pingbing Ming
We propose a deep learning based method for simulating the large bending deformation of bilayer plates. Inspired by the greedy algorithm, we propose a pre-training method on a seri…
Error Estimate of Multiscale Finite Element Method for Periodic Media Revisited
Pingbing Ming, Siqi Song
We derive the optimal energy error estimate for multiscale finite element method with oversampling technique applying to elliptic system with rapidly oscillating periodic coefficie…
Taylor-Hood like finite elements for nearly incompressible strain gradient elasticity problems
Yulei Liao, Pingbing Ming, Yun Xu
We propose a family of mixed finite elements that are robust for the nearly incompressible strain gradient model, which is a fourth-order singular perturbed elliptic system. The el…
A Nitsche Hybrid multiscale method with non-matching grids
Pingbing Ming, Siqi Song
We propose a Nitsche method for multiscale partial differential equations, which retrieves the macroscopic information and the local microscopic information at one stroke. We prove…
An Efficient Online-Offline Method for Elliptic Homogenization Problems
Yufang Huang, Pingbing Ming, Siqi Song
We present a new numerical method for solving the elliptic homogenization problem. The main idea is that the missing effective matrix is reconstructed by solving the local least-sq…
Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions
Yulei Liao, Pingbing Ming
We propose a new method to deal with the essential boundary conditions encountered in the deep learning-based numerical solvers for partial differential equations. The trial functi…
New Nonconforming Elements for Linear Strain Gradient Elastic Model
Hongliang Li, Pingbing Ming, Zhong-ci Shi
Based on a new HKorn's inequality, we propose new nonconforming elements for the linear strain gradient elastic model. The first group of elements are Hconforming but H$^…
An Arbitrary-Order Discontinuous Galerkin Method with One Unknown Per Element
Ruo Li, Pingbing Ming, Zhiyuan Sun +1
We propose an arbitrary-order discontinuous Galerkin method for second-order elliptic problem on general polygonal mesh with only one degree of freedom per element. This is achieve…
A Discontinuous Galerkin Method by Patch Reconstruction for Biharmonic Problem
Ruo Li, Pingbing Ming, Zhiyuan Sun +2
We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed metho…
A Concurrent Global-local Numerical Method for Multiscale PDEs
Yufang Huang, Jianfeng Lu, Pingbing Ming
We present a new hybrid numerical method for multiscale partial differential equations, which simultaneously captures the global macroscopic information and resolves the local micr…
Two robust nonconforming Helements for linear strain gradient elasticity
Hongliang Li, Pingbing Ming, Zhong-ci Shi
We propose two nonconforming finite elements to approximate a boundary value problem arising from strain gradient elasticity, which is a higher-order perturbation of the linearized…
A multiscale finite element method for oscillating Neumann problem on rough domain
P. B. Ming, X. Xu
We develop a new multiscale finite element method for Laplace equation with oscillating Neumann boundary conditions on rough boundaries. The key point is the introduction of a new…
A study on the quasiconinuum approximations of a one-dimensional fracture model
Xiantao Li, Pingbing Ming
We study three quasicontinuum approximations of a lattice model for crack propagation. The influence of the approximation on the bifurcation patterns is investigated. The estimate…
Stability of a force-based hybrid method with planar sharp interface
Jianfeng Lu, Pingbing Ming
We study a force-based hybrid method that couples atomistic model with Cauchy-Born elasticity model with sharp transition interface. We identify stability conditions that guarantee…
On the effect of ghost force in the quasicontinuum method: dynamic problems in one dimension
Xiantao Li, Pingbing Ming
Numerical error induced by the "ghost forces" in the quasicontinuum method is studied in the context of dynamic problems. The error in the ({W}^{1,\infty}) norm is analyzed for the…
Ghost Force Influence of a Quasicontinuum Method in Two Dimension
Jingrun Chen, Pingbing Ming
We derive an analytical expression for the solution of a two-dimensional quasicontinuum method with a planar interface. The expression is used to prove that the ghost force may lea…
Convergence of a force-based hybrid method for atomistic and continuum models in three dimension
Jianfeng Lu, Pingbing Ming
We study a force-based hybrid method that couples atomistic models with nonlinear Cauchy-Born elasticity models. We show that the proposed scheme converges quadratically to the sol…