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08/29/2023
Optimal error bounds on time-splitting methods for the nonlinear Schrödinger equation with low regularity potential and nonlinearity
We establish optimal error bounds on time-splitting methods for the nonl...
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02/18/2023
Optimal error bounds on the exponential wave integrator for the nonlinear Schrödinger equation with low regularity potential and nonlinearity
We establish optimal error bounds for the exponential wave integrator (E...
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01/08/2023
Error estimates of the time-splitting methods for the nonlinear Schrödinger equation with semi-smooth nonlinearity
We establish error bounds of the Lie-Trotter time-splitting sine pseudos...
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11/01/2022
A structure-preserving parametric finite element method for geometric flows with anisotropic surface energy
We propose and analyze structure-preserving parametric finite element me...
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10/28/2022
Regularized numerical methods for the nonlinear Schrödinger equation with singular nonlinearity
We present different regularizations and numerical methods for the nonli...
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06/04/2022
A symmetrized parametric finite element method for anisotropic surface diffusion ii. three dimensions
For the evolution of a closed surface under anisotropic surface diffusio...
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03/11/2022
Improved uniform error bounds on time-splitting methods for the long-time dynamics of the weakly nonlinear Dirac equation
Improved uniform error bounds on time-splitting methods are rigorously p...
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02/14/2022
A structure-preserving finite element approximation of surface diffusion for curve networks and surface clusters
We consider the evolution of curve networks in two dimensions (2d) and s...
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12/07/2021
Improved uniform error bounds on time-splitting methods for the long-time dynamics of the Dirac equation with small potentials
We establish improved uniform error bounds on time-splitting methods for...
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12/01/2021
A symmetrized parametric finite element method for anisotropic surface diffusion of closed curves via a Cahn-Hoffman -vector formulation
We deal with a long-standing problem about how to design an energy-stabl...
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11/26/2021
Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations
We propose and analyze volume-preserving parametric finite element metho...
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09/30/2021
Improved uniform error bounds on time-splitting methods for long-time dynamics of the nonlinear Klein–Gordon equation with weak nonlinearity
We establish improved uniform error bounds on time-splitting methods for...
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09/18/2021
Improved uniform error bounds for the time-splitting methods for the long-time dynamics of the Schrödinger/nonlinear Schrödinger equation
We establish improved uniform error bounds for the time-splitting method...
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04/03/2021
A structure-preserving parametric finite element method for surface diffusion
We propose a structure-preserving parametric finite element method (SP-P...
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12/21/2020
An Energy-Stable Parametric Finite Element Method for Simulating Solid-state Dewetting Problems in Three Dimensions
We propose an accurate and energy-stable parametric finite element metho...
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12/10/2020
An energy-stable parametric finite element method for anisotropic surface diffusion
We propose an energy-stable parametric finite element method (ES-PFEM) t...
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06/09/2020
Error estimates of energy regularization for the logarithmic Schrodinger equation
The logarithmic nonlinearity has been used in many partial differential ...
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03/03/2020
An energy-stable parametric finite element method for simulating solid-state dewetting
We propose an energy-stable parametric finite element method (ES-PFEM) f...
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01/29/2020
Uniform error bounds of a time-splitting spectral method for the long-time dynamics of the nonlinear Klein-Gordon equation with weak nonlinearity
We establish uniform error bounds of a time-splitting Fourier pseudospec...
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10/27/2019
A Jacobi spectral method for computing eigenvalue gaps and their distribution statistics of the fractional Schrödinger operator
We propose a spectral method by using the Jacobi functions for computing...
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08/24/2019
Computing ground states of Bose-Einstein Condensates with higher order interaction via a regularized density function formulation
We propose and analyze a new numerical method for computing the ground s...
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06/25/2019