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• W3209503845 startingPage "114220" @default.
• W3209503845 abstract "In this article, we present a theoretical framework for integrating discontinuous Galerkin methods in the variational multiscale paradigm. Our starting point is a projector-based multiscale decomposition of a generic variational formulation that uses broken Sobolev spaces and Lagrange multipliers to accommodate the non-conforming nature at the boundaries of discontinuous Galerkin elements. We show that existing discontinuous Galerkin formulations, including their penalty terms, follow immediately from a specific choice of multiscale projector. We proceed by defining the “fine-scale closure function”, which captures the closure relation between the remaining fine-scale term in the discontinuous Galerkin formulation and the coarse-scale solution via a single integral expression for each basis function in the coarse-scale test space. We show that the projectors that correspond to discontinuous Galerkin methods lead to fine-scale closure functions with more compact support and smaller amplitudes compared to the fine-scale closure function of the classical (conforming) finite element method. This observation provides a new perspective on the natural stability of discontinuous Galerkin methods for hyperbolic problems, and may open the door to rigorously designed variational multiscale based fine-scale models that are suitable for DG methods." @default.
• W3209503845 created "2021-11-08" @default.
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• W3209503845 date "2022-01-01" @default.
• W3209503845 modified "2023-10-16" @default.
• W3209503845 title "Discontinuous Galerkin methods through the lens of variational multiscale analysis" @default.
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• W3209503845 doi "https://doi.org/10.1016/j.cma.2021.114220" @default.
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