A Provably Positive Discontinuous Galerkin Method for Multidimensional Ideal Magnetohydrodynamics
A Provably Positive Discontinuous Galerkin Method for Multidimensional Ideal Magnetohydrodynamics is a scholarly work, published in 2018 in ''SIAM Journal on Scientific and Statistical Computing''. The main subjects of the publication include computational fluid dynamics, finite element method, and numerical method for ordinary differential equations. The authors first\ndevelop uniformly high-order discontinuous Galerkin (DG) schemes which provably\npreserve the positivity of density and pressure for multidimensional ideal MHD.\nThe schemes are constructed by using the locally divergence-free DG schemes for\nthe symmetrizable ideal MHD equations as the base schemes, a PP limiter to\nenforce the positivity of the DG solutions, and the strong stability preserving\nmethods for time discretization.