11 citations · 20 across the 10 of their papers we have counts for
11 papers
Error Analysis of the Inverse Conductivity Problem with Scattered Measurements
Bangti Jin, Qimeng Quan, Wenlong Zhang
In this work, we investigate the inverse problem of recovering the conductivity coefficient in an elliptic equation from noisy measurements collected at finitely many deterministic…
Conditional Stability and Numerical Reconstruction of a Parabolic Inverse Source Problem Using Carleman Estimates
Tianhao Hu, Xinchi Huang, Bangti Jin +2
In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We estab…
Numerical Analysis of Unsupervised Learning Approaches for Parameter Identification in PDEs
Siyu Cen, Bangti Jin, Qimeng Quan +1
Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches…
Stochastic Convergence Analysis of Inverse Potential Problem
Bangti Jin, Qimeng Quan, Wenlong Zhang
In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling…
Regularity Analysis and High-Order Time Stepping Scheme for Quasilinear Subdiffusion
Bangti Jin, Qimeng Quan, Barbara Wohlmuth +1
In this work, we investigate a quasilinear subdiffusion model which involves a fractional derivative of order in time and a nonlinear diffusion coefficient. First, usi…
Numerical Recovery of the Diffusion Coefficient in Diffusion Equations from Terminal Measurement
Bangti Jin, Xiliang Lu, Qimeng Quan +1
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigo…
Conductivity Imaging from Internal Measurements with Mixed Least-Squares Deep Neural Networks
Bangti Jin, Xiyao Li, Qimeng Quan +1
In this work we develop a novel approach using deep neural networks to reconstruct the conductivity distribution in elliptic problems from one measurement of the solution over the…
Hybrid Neural-Network FEM Approximation of Diffusion Coefficient in Elliptic and Parabolic Problems
Siyu Cen, Bangti Jin, Qimeng Quan +1
In this work we investigate the numerical identification of the diffusion coefficient in elliptic and parabolic problems using neural networks. The numerical scheme is based on the…
Convergence Rate Analysis of Galerkin Approximation of Inverse Potential Problem
Bangti Jin, Xiliang Lu, Qimeng Quan +1
In this work we analyze the inverse problem of recovering the space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish no…
Analysis of Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Conditions
Chenguang Duan, Yuling Jiao, Yanming Lai +3
Deep Ritz methods (DRM) have been proven numerically to be efficient in solving partial differential equations. In this paper, we present a convergence rate in norm for dee…
Lowest-degree piecewise polynomial de Rham complex on general quadrilateral grids
Qimeng Quan, Xia Ji, Shuo Zhang
This paper is devoted to the construction of finite elements on grids that consist of general quadrilaterals not limited in parallelograms. Two finite elements defined as Ciarlet's…