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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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- Nonlinear parabolic equations and phase field equation
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Convergence of multistep projection methods for harmonic map heat flows into general surfaces
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Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations
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A high-order exponential integrator for nonlinear parabolic equations with nonsmooth initial data
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A second-order stabilization method for linearizing and decoupling nonlinear parabolic systems
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- Energy-decaying extrapolated RK-SAV methods for the Allen-Cahn and Cahn-Hilliard equations
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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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