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07/14/2023
High-order splitting finite element methods for the subdiffusion equation with limited smoothing property
In contrast with the diffusion equation which smoothens the initial data...
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06/08/2023
A new framework for the analysis of finite element methods for fluid-structure interaction problems
Finite element methods and kinematically coupled schemes that decouple t...
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05/08/2023
Improved error estimates for a modified exponential Euler method for the semilinear stochastic heat equation with rough initial data
A class of stochastic Besov spaces B^p L^2(Ω;Ḣ^α(𝒪)), 1≤ p≤∞ and α∈[-2,2...
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03/16/2023
Weak discrete maximum principle of isoparametric finite element methods in curvilinear polyhedra
The weak maximum principle of the isoparametric finite element method is...
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06/28/2022
Optimal analysis of finite element methods for the stochastic Stokes equations
Numerical analysis for the stochastic Stokes/Navier-Stokes equations is ...
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06/19/2022
An unfiltered low-regularity integrator for the KdV equation with solutions below H^1
This article is concerned with the construction and analysis of new time...
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03/29/2022
A second-order low-regularity correction of Lie splitting for the semilinear Klein–Gordon equation
The numerical approximation of the semilinear Klein–Gordon equation in t...
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07/28/2021
A semi-implicit low-regularity integrator for Navier-Stokes equations
A new type of low-regularity integrator is proposed for Navier-Stokes eq...
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06/15/2021
Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems
Maximal parabolic L^p-regularity of linear parabolic equations on an evo...
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01/31/2021
A perimeter-decreasing and area-conserving algorithm for surface diffusion flow of curves
A fully discrete finite element method, based on a new weak formulation ...
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01/11/2021
A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation
A fully discrete and fully explicit low-regularity integrator is constru...
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01/11/2021
Convergence of Dziuk's semidiscrete finite element method for mean curvature flow of closed surfaces with high-order finite elements
Dziuk's surface finite element method for mean curvature flow has had si...
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01/07/2021
Analysis of fully discrete finite element methods for 2D Navier–Stokes equations with critical initial data
First-order convergence in time and space is proved for a fully discrete...
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11/16/2020
A high-order exponential integrator for nonlinear parabolic equations with nonsmooth initial data
A variable stepsize exponential multistep integrator, with contour integ...
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10/17/2020
Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations
A new class of high-order maximum principle preserving numerical methods...
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07/30/2020
A convergent evolving finite element algorithm for Willmore flow of closed surfaces
A proof of convergence is given for a novel evolving surface finite elem...
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07/27/2020
A convergent post-processed discontinuous Galerkin method for incompressible flow with variable density
A linearized semi-implicit unconditionally stable decoupled fully discre...
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06/09/2020
High-order mass- and energy-conserving SAV-Gauss collocation finite element methods for the nonlinear Schrödinger equation
A family of arbitrarily high-order fully discrete space-time finite elem...
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05/04/2020
Maximal regularity of multistep fully discrete finite element methods for parabolic equations
This article extends the semidiscrete maximal L^p-regularity results in ...
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04/23/2020
Subdiffusion with Time-Dependent Coefficients: Improved Regularity and Second-Order Time Stepping
This article concerns second-order time discretization of subdiffusion e...
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12/11/2019
A convergent algorithm for mean curvature flow driven by diffusion on the surface
The evolution of a closed two-dimensional surface driven by both mean cu...
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09/15/2019