My research interest is numerical analysis for partial differential equations, in particular, the finite element method (FEM). I am interseted in discrete counterparts of certain properties of the original problems and thier applications to error analysis for numerical solutions of (nonlinear) PDEs. Moreover, I have been studying some problems on elastic curves and fluid dynamics. The details of my research topics are listed as follows.
- Discrete maximum principle for elliptic problems for FEM
- Discrete maximal regularity (DMR) for parabolic problems for FEM
- Discrete counterpart of analytic semigroups for FEM
- Error analysis for FEM of semilinear parabolic equations via DMR
- Energy dissipative numerical schemes for gradient flows
- Numerical analysis for elastica under non-standard constraints
- Finite element method for the hydrostatoc Stokes equations