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DISCONTINUOUS GALERKIN METHODS FOR THE MULTI-DIMENSIONAL VLASOV–POISSON PROBLEM

Centre de Recerca Matemàtica (CRM), 08193 Bellaterra, Barcelona, Spain

Institució Catalana de Recerca i Estudis Avançats, and Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain

On leave from: Department of Mathematics, Imperial College London, London SW7 2AZ, UK.

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, and

CHI-WANG SHU

Division of Applied Mathematics, Brown University, Providence, RI 16802, USA

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https://doi.org/10.1142/S021820251250042XCited by:32 (Source: Crossref)

Abstract

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov–Poisson system. The schemes are constructed by combining a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

Keywords:

AMSC: Primary 65N30, Secondary 65M60, Secondary 65M12, Secondary 65M15, Secondary 82D10

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