TY - JOUR
T1 - A numerical approach to solving an inverse parabolic problem using finite differential method
AU - 
JO - Journal of Information and Computing Science
VL - 3
SP - 215
EP - 224
PY - 2024
DA - 2024/01
SN - 3
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22770.html
KW - finite element, numerical analysis, Euler equation. 

AB - Runge-Kutta discontinuous Galerkin (RKDG) finite element method for hyperbolic conservation 
laws is a high order method, which can handle complicated geometries flexibly and treat boundary conditions 
easily.  In  this  paper,  we  propose  a  new  numerical  method  for  treating  interface  using  the  advantages  of 
RKDG finite element method. We use level set method to track the moving interface. In every time step, a 
Riemann problem at the interface is defined. The two cells adjacent to the interface are computed using the 
Riemann problem solver. If the interface crosses a cell in the next time step, the values of the flow variables 
of the cell crossed are modified through linear interpolation. Othewise, we do nothing.