Conservative Discontinuous Galerkin/Hermite Spectral Method for the Vlasov–Poisson System

A Conservative Discontinuous Galerkin Method for the Degasperis–procesi Equation

In this work, we design, analyze and test a conservative discontinuous Galerkin method for solving the Degasperis–Procesi equation. This model is integrable and admits possibly discontinuous solutions, and therefore suitable for modeling both short wave breaking and long wave propagation phenomena. The proposed numerical method is high order accurate, and preserves two invariants, mass and ener...

A Discontinuous Spectral Element Method for the Level Set Equation

Inverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions

In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

Energy conserving discontinuous Galerkin spectral element method for the Vlasov-Poisson system

We propose a new, energy conserving, spectral element, discontinuous Galerkin method for the approximation of the Vlasov–Poisson system in arbitrary dimension, using Cartesian grids. The method is derived from the one proposed in [ACS12], with two modifications: energy conservation is obtained by a suitable projection operator acting on the solution of the Poisson problem, rather than by solvin...

SimulatingMagnetohydrodynamic Instabilitieswith Conservative Perturbed MHDModel Using Discontinuous Galerkin Method

In magnetically confined plasma research, the understandings of small and large perturbations at equilibrium are both critical for plasma controlling and steady state operation. Numerical simulations using original MHD model can hardly give clear picture for small perturbations, while non-conservative perturbed MHD model may break conservation law, and give unphysical results when perturbations...