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Numerical methods and analysis for partial differential equations, including
- Surface evolution under geometric flows, geometric evolution equations, PDEs on surfaces
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- Fluid-structure interation and moving interface problems
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- Low-regularity approximation to nonlinear dispersive equations
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- Incompressible Navier–Stokes equations
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Optimal analysis of finite element methods for the stochastic Stokes equations
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Optimal convergence of the arbitrary Lagrangian–Eulerian interface tracking method for two-phase Navier–Stokes flow without surface tension
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A bounded numerical solution with a small mesh size implies existence of a smooth solution to the Navier–Stokes equations
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A semi-implicit exponential low-regularity integrator for the Navier-Stokes equations
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Analysis of fully discrete finite element methods for 2D Navier-Stokes equations with critical initial data
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Second-order convergence of the linearly extrapolated Crank–Nicolson method for the Navier-Stokes equations with H1 initial data
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A convergent post-processed discontinuous Galerkin method for incompressible flow with variable density
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- Nonlinear parabolic equations and phase field equation
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- Interior penalty finite element methods and perfectly matched layer (PML) for the Helmholtz equation
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- Maximal Lp-regularity of time discretization methods for parabolic equations
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- Maximum-norm stability and maximal Lp-regularity of finite element methods
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- High-order approximation of singular solutions of fractional evolution equations
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- Dynamic Ginzburg–Landau superconductivity equations in nonsmooth domains
- Time-dependent Joule heating problem (for thermistors with temperature-dependent electric conductivity
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