Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm
MetadataShow full item record
We investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numerically compare coarse-mesh accuracy of the approximation when using the quasi-optimal norm, the standard norm, and the weighted norm. Our results show that the quasi-optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions. We address the problems associated to the resolution of the optimal test functions with respect to the quasi-optimal norm by studying their convergence numerically. In order to facilitate understanding of the method, we also include a detailed explanation of the methodology from the algorithmic point of view. © 2013 Elsevier Ltd. All rights reserved.
Showing items related by title, author, creator and subject.
Yu, Changjun (2012)In this thesis, We propose new computational algorithms and methods for solving four classes of constrained optimization and optimal control problems. In Chapter 1, we present a brief review on optimization and ...
Tseng, Chien H. (1999)The design of envelope-constrained (EC) filters is considered for the time-domain synthesis of filters for signal processing problems. The objective is to achieve minimal noise enhancement where the shape of the filter ...
A class of discontinuous Petrov-Galerkin methods. Part IV: The optimal test norm and time-harmonic wave propagation in 1DZitelli, J.; Muga, I.; Demkowicz, L.; Gopalakrishnan, J.; Pardo, D.; Calo, Victor (2011)The phase error, or the pollution effect in the finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems in the high-frequency range. This paper presents ...