This thesis contains two parts, including the development of a modified total variation bounded (TVB) limiter applied to the discontinuous Galerkin (DG) methods, and the …
This dissertation consists of three topics on bound-preserving discontinuous Galerkin (DG) methods for time-dependent and stationary hyperbolic equations, and efficient finite difference weighted essentially non-oscillatory …
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 …