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We are interested in developing a numerical method for capturing stationarysheaths, that a plasma forms in contact with a metallic wall. This work isbased on a bi-species (ion/electron) Vlasov-Amp{\`e}re model proposed in [3].The main question addressed in this work is to know if classical numericalschemes can preserve stationary solutions with boundary conditions, since thesesolutions are not a priori conserved at the discrete level. In the context ofhigh-order semi-Lagrangian method, due to their large stencil, interpolationnear the boundary of the domain requires also a specific treatment.

Numerical stability of plasma sheath