A subcell-enriched Galerkin method for advection problems

• Verfasst von: Rupp, Andreas [VerfasserIn]
• Verfasst von: Hauck, Moritz [VerfasserIn]
• Verfasst von: Aizinger, Vadym [VerfasserIn]
• Titel: A subcell-enriched Galerkin method for advection problems
• Verf.angabe: Andreas Rupp, Moritz Hauck, Vadym Aizinger
• E-Jahr: 2021
• Jahr: 22 April 2021
• Umfang: 10 S.
• Teil: volume:93
• Teil: year:2021
• Teil: pages:120-129
• Teil: extent:10
• Fussnoten: Gesehen am 29.07.2021
• Titel Quelle: Enthalten in: Computers and mathematics with applications
• Ort Quelle: Amsterdam [u.a.] : Elsevier Science, 1975
• Jahr Quelle: 2021
• Band/Heft Quelle: 93(2021), Seite 120-129
• ISSN Quelle: 1873-7668
• DOI: doi:10.1016/j.camwa.2021.04.010
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Advection equation
• Sach-SW: Arbitrary order finite elements
• Sach-SW: Discontinuous Galerkin method
• Sach-SW: Enriched Galerkin method
• Sach-SW: Hyperbolic equation
• Sach-SW: Subcell enrichment
• K10plus-PPN: 1764919882

Abstract

In this work, we introduce a generalization of the enriched Galerkin (EG) method. The key feature of our scheme is an adaptive two-mesh approach that, in addition to the standard enrichment of a conforming finite element discretization via discontinuous degrees of freedom, allows to subdivide selected (e.g. troubled) mesh cells in a non-conforming fashion and to use further discontinuous enrichment on this finer submesh. We prove stability and sharp a priori error estimates for a linear advection equation by using a specially tailored projection and conducting some parts of a standard convergence analysis for both meshes. By allowing an arbitrary degree of enrichment on both, the coarse and the fine mesh (also including the case of no enrichment), our analysis technique is very general in the sense that our results cover the range from the standard continuous finite element method to the standard discontinuous Galerkin (DG) method with (or without) local subcell enrichment. Numerical experiments confirm our analytical results and indicate good robustness of the proposed method.