Demkowicz was supported in part by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615], and by a research contract with Boeing. Gopalakrishnan was supported in part by the National Science Foundation under grant DMS-0713833. Niemi was supported in part by KAUST.
Applied Numerical Mathematics
Discontinuous functions, Numerical analysis, Diffusion processes, Matrices -- Norms, Reaction-diffusion equations
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: for 1D and for 2D problems. The adaptive process is fully automatic and starts with a mesh consisting of few elements only.
Copyright 2012 Published by Elsevier B.V.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Locate the Document
Published as: Demkowicz, L., Gopalakrishnan, J., & Niemi, A. H. (2012). A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity. Applied numerical mathematics, 62(4), 396-427.