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Convergence of shock capturing schemes for the compressible Euler-Poisson equations. (English) Zbl 0858.76051
Summary: 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 are proved with the aid of the compensated compactness method. Then new existence results for 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 $$L^\infty$$ bounds.
Reviewer: Reviewer (Berlin)

##### MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 76L05 Shock waves and blast waves in fluid mechanics 35Q35 PDEs in connection with fluid mechanics 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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