209 citations · 274 across the 22 of their papers we have counts for
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Numerical Approximation and Analysis of the Inverse Robin Problem Using the Kohn-Vogelius Method
Erik Burman, Siyu Cen, Bangti Jin +1
In this work, we numerically investigate the inverse Robin problem of recovering a piecewise constant Robin coefficient in an elliptic or parabolic problem from the Cauchy data on…
Numerical Reconstruction and Analysis of Backward Semilinear Subdiffusion Problems
Xu Wu, Jiang Yang, Zhi Zhou
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditi…
Point Source Identification Using Singularity Enriched Neural Networks
Tianhao Hu, Bangti Jin, Zhi Zhou
The inverse problem of recovering point sources represents an important class of applied inverse problems. However, there is still a lack of neural network-based methods for point…
Inverse Problems for Subdiffusion from Observation at an Unknown Terminal Time
Bangti Jin, Yavar Kian, Zhi Zhou
Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal obser…
Backward diffusion-wave problem: stability, regularization and approximation
Zhengqi Zhang, Zhi Zhou
We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusion-wave problem, which involves a fractional derivative in time with o…
Robust Convergence of Parareal Algorithms with Arbitrarily High-order Fine Propagators
Jiang Yang, Zhaoming Yuan, Zhi Zhou
The aim of this paper is to analyze the robust convergence of a class of parareal algorithms for solving parabolic problems. The coarse propagator is fixed to the backward Euler me…
Arbitrarily High-order Maximum Bound Preserving Schemes with Cut-off Postprocessing for Allen-Cahn Equations
Jiang Yang, Zhaoming Yuan, Zhi Zhou
We develop and analyze a class of maximum bound preserving schemes for approximately solving Allen--Cahn equations. We apply a th-order single-step scheme in time (where the non…
Reconstruction of a Space-Time Dependent Source in Subdiffusion Models via a Perturbation Approach
Bangti Jin, Yavar Kian, Zhi Zhou
In this article we study inverse problems of recovering a space-time dependent source component from the lateral boundary observation in a subidffusion model. The mathematical mode…
Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations
Buyang Li, Jiang Yang, Zhi Zhou
A new class of high-order maximum principle preserving numerical methods is proposed for solving parabolic equations, with application to the semilinear Allen--Cahn equation. The p…
Error Analysis of Finite Element Approximations of Diffusion Coefficient Identification for Elliptic and Parabolic Problems
Bangti Jin, Zhi Zhou
In this work, we present a novel error analysis for recovering a spatially dependent diffusion coefficient in an elliptic or parabolic problem. It is based on the standard regulari…
An Inverse Potential Problem for Subdiffusion: Stability and Reconstruction
Bangti Jin, Zhi Zhou
In this work, we study the inverse problem of recovering a potential coefficient in the subdiffusion model, which involves a Djrbashian-Caputo derivative of order in ti…
Numerical Analysis of Backward Subdiffusion Problems
Zhengqi Zhang, Zhi Zhou
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time…
The energy technique for the six-step BDF method
Georgios Akrivis, Minghua Chen, Fan Yu +1
In combination with the Grenander--Szegö theorem, we observe that a relaxed positivity condition on multipliers, milder than the basic %fundamental requirement of the Nevanlinna--O…
Subdiffusion with Time-Dependent Coefficients: Improved Regularity and Second-Order Time Stepping
Bangti Jin, Buyang Li, Zhi Zhou
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates a…
Nonlocal-in-time dynamics and crossover of diffusive regimes
Qiang Du, Zhi Zhou
We study a simple nonlocal-in-time dynamic system proposed for the effective modeling of complex diffusive regimes in heterogeneous media. We present its solutions and their common…
High-order Time Stepping Schemes for Semilinear Subdiffusion Equations
Kai Wang, Zhi Zhou
The aim of this paper is to develop and analyze high-order time stepping schemes for solving semilinear subdiffusion equations. We apply the -step BDF convolution quadrature to…
Numerical methods for nonlocal and fractional models
Marta D'Elia, Qiang Du, Christian Glusa +3
Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swa…
Numerical Estimation of a Diffusion Coefficient in Subdiffusion
Bangti Jin, Zhi Zhou
In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involv…
Time-Fractional Allen-Cahn Equations: Analysis and Numerical Methods
Qiang Du, Jiang Yang, Zhi Zhou
In this work, we consider a time-fractional Allen-Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order $α\in(0…
Incomplete Iterative Solution of the Subdiffusion Problem
Bangti Jin, Zhi Zhou
In this work, we develop an efficient incomplete iterative scheme for the numerical solution of the subdiffusion model involving a Caputo derivative of order in time. I…