Geodesic
Theoretical and numerical studies of the $P_NP_M$ DG schemes in one space dimension
Applications of Mathematics, Tome 64 (2019) no. 6, pp. 599-635.

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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.
DOI : 10.21136/AM.2019.0226-18
Classification : 33C45, 65M12, 65M60
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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     title = {Theoretical and numerical studies of the $P_NP_M$ {DG} schemes in one space dimension},
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Badenjki, Abdulatif; Warnecke, Gerald. Theoretical and numerical studies of the $P_NP_M$ DG schemes in one space dimension. Applications of Mathematics, Tome 64 (2019) no. 6, pp. 599-635. doi : 10.21136/AM.2019.0226-18. http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0226-18/

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