Applications of Mathematics, Vol. 64, No. 6, pp. 599-635, 2019
Theoretical and numerical studies of the $P_NP_M$ DG schemes in one space dimension
Abdulatif Badenjki, Gerald Warnecke
Received August 18, 2018. Published online November 20, 2019.
Abstract: We give a proof of the existence of a solution of reconstruction operators used in the $P_NP_M$ DG schemes in one space dimension. Some properties and error estimates of the projection and reconstruction operators are presented. Then, by applying the $P_NP_M$ DG schemes to the linear advection equation, we study their stability obtaining maximal limits of the Courant numbers for several $P_NP_M$ DG schemes mostly experimentally. A numerical study explains how the stencils used in the reconstruction affect the efficiency of the schemes.
Keywords: $P_NP_M$ DG scheme; piecewise polynomial; projection; reconstruction; least square; local continuous space time Galerkin method; discontinuous Galerkin; advection equation; conservation law; von Neumann stability analysis; time discretization
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Affiliations: Abdulatif Badenjki, Gerald Warnecke, Institute for Analysis and Numerics, Otto-von-Guericke University, Universitaetsplatz 2, 39106 Magdeburg, Germany, e-mail: a.badenjki@hotmail.com, warnecke@ovgu.de
