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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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- Maximum-norm stability and maximal Lp-regularity of finite element methods
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Weak maximum principle of finite element methods for parabolic equations in polygonal domains
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Weak discrete maximum principle of isoparametric finite element methods in curvilinear polyhedra.
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Maximum-norm stability of the finite element method for the Neumann problem in nonconvex polygons with locally refined mesh
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Maximal regularity of multistep fully discrete finite element methods for parabolic equations
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- Analyticity, maximal regularity and maximum-norm stability of FEM for parabolic equations in nonconvex polyhedra
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- Maximal Lp error analysis of FEMs for nonlinear parabolic equations with nonsmooth coefficients
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- Maximal Lp analysis of FEM for parabolic equations with nonsmooth coefficients in convex polyhedra
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- Maximum-norm stability and maximal Lp regularity of FEMs for parabolic equations with Lipschitz continuous coefficients
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