@article{Cotter:2016:10.1016/j.jcp.2016.02.021, author = {Cotter, CJ and Kuzmin, D}, doi = {10.1016/j.jcp.2016.02.021}, journal = {Journal of Computational Physics}, pages = {363--373}, title = {Embedded discontinuous Galerkin transport schemes with localised limiters}, url = {http://dx.doi.org/10.1016/j.jcp.2016.02.021}, volume = {311}, year = {2016} }
TY - JOUR AB - Motivated by finite element spaces used for representation of temperature in the compatible fi-nite element approach for numerical weather prediction, we introduce locally bounded transportschemes for (partially-)continuous finite element spaces. The underlying high-order transportscheme is constructed by injecting the partially-continuous field into an embedding discontinuousfinite element space, applying a stable upwind discontinuous Galerkin (DG) scheme, and projectingback into the partially-continuous space; we call this an embedded DG transport scheme. Weprove that this scheme is stable in L2 provided that the underlying upwind DG scheme is. Wethen provide a framework for applying limiters for embedded DG transport schemes. StandardDG limiters are applied during the underlying DG scheme. We introduce a new localised form ofelement-based flux-correction which we apply to limiting the projection back into the partiallycontinuousspace, so that the whole transport scheme is bounded. We provide details in the specificcase of tensor-product finite element spaces on wedge elements that are discontinuous P1/Q1 inthe horizontal and continuous P2 in the vertical. The framework is illustrated with numericaltests. AU - Cotter,CJ AU - Kuzmin,D DO - 10.1016/j.jcp.2016.02.021 EP - 373 PY - 2016/// SN - 0021-9991 SP - 363 TI - Embedded discontinuous Galerkin transport schemes with localised limiters T2 - Journal of Computational Physics UR - http://dx.doi.org/10.1016/j.jcp.2016.02.021 UR - https://www.sciencedirect.com/science/article/pii/S0021999116000759?via%3Dihub UR - http://hdl.handle.net/10044/1/29387 VL - 311 ER -
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