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03/21/2023
Convergence analysis of a positivity-preserving numerical scheme for the Cahn-Hilliard-Stokes system with Flory-Huggins energy potential
A finite difference numerical scheme is proposed and analyzed for the Ca...
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09/27/2022
Phase field modeling and computation of vesicle growth or shrinkage
We present a phase field model for vesicle growth or shrinkage induced b...
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08/12/2022
A second order accurate numerical method for the Poisson-Nernst-Planck system in the energetic variational formulation
A second order accurate (in time) numerical scheme is proposed and analy...
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05/19/2021
Convergence analysis of the variational operator splitting scheme for a reaction-diffusion system with detailed balance
We present a detailed convergence analysis for an operator splitting sch...
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04/29/2021
A positivity-preserving, energy stable scheme for a Ternary Cahn-Hilliard system with the singular interfacial parameters
In this paper, we construct and analyze a uniquely solvable, positivity ...
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04/19/2021
An energy stable finite element scheme for the three-component Cahn-Hilliard-type model for macromolecular microsphere composite hydrogels
In this article, we present and analyze a finite element numerical schem...
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12/22/2020
Structure-preserving, energy stable numerical schemes for a liquid thin film coarsening model
In this paper, two finite difference numerical schemes are proposed and ...
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09/17/2020
A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system
In this paper we propose and analyze a finite difference numerical schem...
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06/11/2020
Preconditioned accelerated gradient descent methods for locally Lipschitz smooth objectives with applications to the solution of nonlinear PDEs
We analyze preconditioned Nesterov's accelerated gradient descent method...
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04/18/2020
Doubly Degenerate Diffuse Interface Models of Anisotropic Surface Diffusion
We extend the doubly degenerate Cahn-Hilliard (DDCH) models for isotropi...
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09/10/2019
Doubly Degenerate Diffuse Interface Models of Surface Diffusion
We discuss two doubly degenerate Cahn-Hilliard (DDCH) models for surface...
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06/28/2019