Paper Info
Title
Embedded discontinuous Galerkin transport schemes with localised limiters.
Abstract
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 L 2 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.
Year
DOI
Venue
2016
10.1016/j.jcp.2016.02.021
J. Comput. Physics
Keywords
Field
DocType
Discontinuous Galerkin,Slope limiters,Flux corrected transport,Convection-dominated transport,Numerical weather prediction
Discontinuous Galerkin method,Mathematical optimization,Embedding,Wedge (mechanical device),Limiter,Finite element method,Flux-corrected transport,Mathematics,Bounded function,Numerical weather prediction
Journal
Volume
Issue
ISSN
311
C
0021-9991
Citations 
PageRank 
References 
4
0.43
9
Authors
2
Name
Order
Citations
PageRank
Colin J. Cotter18814.52
Dmitri Kuzmin216723.90