Convergence of shock capturing schemes for the compressible Euler-Poisson equations

We are concerned with approximate methods to construct global solutions with geometrical structure to the compressible Euler-Poisson equations in several space variables. A shock capturing numerical scheme is introduced to overcome the new difficulties from the nonlinear resonance of the system and the nonlocal behavior of the source terms. The convergence and consistency of the shock capturing scheme for the equations is proved with the aid of the compensated compactness method. Then new existence results of the global solutions with geometrical structure are obtained. The traces of the weak solutions are defined and then the weak solutions are proved to satisfy the boundary conditions. The initial data are arbitrarily large with L(infinity) bounds.