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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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- 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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Weak maximum principle of finite element methods for parabolic equations in polygonal domains
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Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems.
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- Maximal regularity of multistep fully discrete finite element methods for parabolic equations
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- Maximal regularity of fully discrete finite element solutions of parabolic equations
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- A-stable time discretizations preserve maximal parabolic regularity
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- Discrete maximal regularity of time-stepping schemes for fractional evolution equations
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- Runge-Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity
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- Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations
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- Maximum norm analysis of implicit-explicit backward difference formulae for nonlinear parabolic equations
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- Maximal regularity of BDF methods for evolving surface PDEs and its application to nonlinear problems
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