293 citations · 1.8k across the 110 of their papers we have counts for
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A Petrov-Galerkin Finite Element Method for Fractional Convection-Diffusion Equations
Bangti Jin, Raytcho Lazarov, Zhi Zhou
In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo deri…
On Nonnegativity Preservation in Finite Element Methods for Subdiffusion Equations
Bangti Jin, Raytcho Lazarov, Vidar Thomée +1
We consider three types of subdiffusion models, namely single-term, multi-term and distributed order fractional diffusion equations, for which the maximum-principle holds and which…
An Analysis of Galerkin Proper Orthogonal Decomposition for Subdiffusion
Bangti Jin, Zhi Zhou
In this work, we develop a novel Galerkin-L1-POD scheme for the subdiffusion model with a Caputo fractional derivative of order in time, which is often used to describ…
Error Estimates for Approximations of Distributed Order Time Fractional Diffusion with Nonsmooth Data
Bangti Jin, Raytcho Lazarov, Dongwoo Sheen +1
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathemat…
A simple finite element method for the boundary value problem with a Riemann-Liouville derivative
Bangti Jin, Raytcho Lazarov, Xiliang Lu +1
We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order on the unit interval . The standard Galerkin finite element…
An analysis of the L1 Scheme for the subdiffusion equation with nonsmooth data
Bangti Jin, Raytcho Lazarov, Zhi Zhou
The subdiffusion equation with a Caputo fractional derivative of order in time arises in a wide variety of practical applications, and it is often adopted to model anom…
A Tutorial on Inverse Problems for Anomalous Diffusion Processes
Bangti Jin, William Rundell
Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At…