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