Details

Autor(en) / Beteiligte

• Cotter, C.J.
• Kuzmin, D.

Titel

Embedded discontinuous Galerkin transport schemes with localised limiters

Ist Teil von

• Journal of computational physics, 2016-04, Vol.311, p.363-373

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2016

Link zum Volltext

Quelle

Elsevier ScienceDirect Journals Complete

Beschreibungen/Notizen

• Motivated by finite element spaces used for representation of temperature in the compatible finite element approach for numerical weather prediction, we introduce locally bounded transport schemes for (partially-)continuous finite element spaces. The underlying high-order transport scheme is constructed by injecting the partially-continuous field into an embedding discontinuous finite element space, applying a stable upwind discontinuous Galerkin (DG) scheme, and projecting back into the partially-continuous space; we call this an embedded DG transport scheme. We prove that this scheme is stable in L2 provided that the underlying upwind DG scheme is. We then provide a framework for applying limiters for embedded DG transport schemes. Standard DG limiters are applied during the underlying DG scheme. We introduce a new localised form of element-based flux-correction which we apply to limiting the projection back into the partially-continuous space, so that the whole transport scheme is bounded. We provide details in the specific case of tensor-product finite element spaces on wedge elements that are discontinuous P1/Q1 in the horizontal and continuous P2 in the vertical. The framework is illustrated with numerical tests.