Retell

Today I want to tell you about two articles on my topic. Both articles deal with moving mesh methods for solving equations in computational physics. The first article was written by Gaburro, Castro, and Dumbser, published in *Monthly Notices of the Royal Astronomical Society* in 2018. The second one was written by Stockie, Mackenzie, and Russell, published in *SIAM Journal on Scientific Computing*. These articles are related to each other because they both describe how to use moving meshes to get better solutions. But the first one is more complex and works in 3D, while the second one focuses on 1D problems.

The first article is about solving Euler equations with gravity on moving meshes. The authors describe a special method that can keep hydrostatic equilibrium exactly. This is very important for astrophysical simulations, like modeling stars. In conclusion, the authors show that their method works well and can capture small changes around equilibrium states.

The second article is about moving mesh methods for 1D conservation laws. The authors explain how to move mesh points to better capture shocks and discontinuities. They use something called equidistribution principle to control mesh motion. The authors draw the conclusion that moving meshes give more accurate results with fewer grid points.

In my opinion, both articles are very useful. The second article gives basic ideas for 1D, and the first article extends these ideas to complex 3D problems. I find these texts very informative for my research. They are directly related to my work on numerical methods with adaptive meshes.