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.
Paszynska, A.; Paszynski, M.; Jopek, K.; Wofniak, M.; Goik, D.; Gurgul, P.; Aboueisha, H.; Moshkov, M.; Calo, Victor; Lenharth, A.; Nguyen, D.; Pingali, K. (2015)We construct quasi-optimal elimination trees for 2D finite element meshes with singularities.These trees minimize the complexity of the solution of the discrete system. The computational cost estimates of the elimination ...
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 ...
Frequency-Dependent Diffusion Constant of Quantum Fluids from Path Integral Monte Carlo and Tikhonov’s Regularizing FunctionalKowalczyk, Poitr; Gauden, P.; Terzyk, A.; Furmaniak, S. (2009)We present a novel implementation of the analytic continuation of the velocity autocorrelation function method that has been developed to study the transport properties of quantum liquids at finite temperatures. To invert ...