Finite element analysis of plasma dust-acoustic waves

For dust acoustic solitary waves, we propose a finite element formulation of the fluid dusty plasma equations. To solve this continuum problem, a Petrov-Galerkin weak form with upwinding is applied. We consider an unmagnetized dusty plasma with negatively charged dust and Boltzmann distributions for electrons and ions. Nonlinearity of ion and electron number density as functions of the electrostatic potential is included. A fully-implicit time-integration is used (backward-Euler method) which requires the derivative of the weak form. A three-field formulation is introduced, with dust number-density, electrostatic potential and dust velocity being the unknown fields. We test the formulation with two numerical (2D and 3D) examples where convergence with mesh size is assessed. These establish the new formulation as a predictive tool in dusty plasmas.