This thesis consists of two topics on discontinuous Galerkin (DG) finite element methods for time-dependent problems. In the first part of the thesis, we analyze …
This thesis consists of two diverse topics on high order numerical methods for time-dependent partial differential equations (PDEs). In the first part, we develop a …
This dissertation presents two topics on numerical solutions solving hyperbolic equations from both theoretical and practical points of view. In the first part, we introduce …
The positivity-preserving property is a highly desirable property when designing high order numerical methods for hyperbolic conservation laws, since negative values sometimes cause ill-posedness of …