Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423261 | Applied Numerical Mathematics | 2012 | 32 Pages |
Abstract
We continue our theoretical and numerical study on the Discontinuous Petrov-Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: ϵ=10â11 for 1D and ϵ=10â7 for 2D problems. The adaptive process is fully automatic and starts with a mesh consisting of few elements only.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Leszek Demkowicz, Jay Gopalakrishnan, Antti H. Niemi,