A subcell-enriched Galerkin method for advection problems
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 select...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
22 April 2021
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| In: |
Computers and mathematics with applications
Year: 2021, Volume: 93, Pages: 120-129 |
| ISSN: | 1873-7668 |
| DOI: | 10.1016/j.camwa.2021.04.010 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.camwa.2021.04.010 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0898122121001425 
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| Author Notes: | Andreas Rupp, Moritz Hauck, Vadym Aizinger |
| Summary: | 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. |
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| Item Description: | Gesehen am 29.07.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1873-7668 |
| DOI: | 10.1016/j.camwa.2021.04.010 |