I am currently involved in mathematical research of various difficulties in numerical PDEs. An article manuscript for the edge-averaged virtual element scheme is in progress. This scheme is a new virtual element method on a polygonal mesh, and it provides stable numerical solutions to convection-diffusion problems in convection-dominated regime. Furthermore, I am researching into ways of improving the numerical dispersion error in the wave equation and Helmholtz equation in two or more dimensions. Through a course on the calculus of variations, I became interested in the Hamiltonian methods in the wave equation in order to find a new way to reduce the dispersion error. I also have valuable experience studying and implementing mixed FEMs, Multi-grid methods, and optimization techniques.
Research Interests
- C0 interior penalty methods for the Gao beam model
- A monotone virtual element scheme
- Pollution errors in the wave equation
- Hamiltonian methods in the wave equation
- Topology optimization