A robust DPG method for convection-dominated diffusion problems II: Adjoint boundary conditions and mesh-dependent test norms

We introduce a DPG method for convection-dominated diffusion problems. The choice of a test norm is shown to be crucial to achieving robust behavior with respect to the diffusion parameter (Demkowicz and Heuer 2011)  [18]. We propose a new inflow boundary condition which regularizes the adjoint prob...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2014-03, Vol.67 (4), p.771-795
Main Authors: Chan, Jesse, Heuer, Norbert, Bui-Thanh, Tan, Demkowicz, Leszek
Format: Article
Language:English
Subjects:
Adaptivity
Convection–diffusion
Finite elements
Higher order
Robustness
Stabilization
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Summary:We introduce a DPG method for convection-dominated diffusion problems. The choice of a test norm is shown to be crucial to achieving robust behavior with respect to the diffusion parameter (Demkowicz and Heuer 2011)  [18]. We propose a new inflow boundary condition which regularizes the adjoint problem, allowing the use of a stronger test norm. The robustness of the method is proven, and numerical experiments demonstrate the method’s robust behavior.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2013.06.010