On the application of mass lumping in the Petrov–Galerkin finite element method for convection-diffusion problems

TitleOn the application of mass lumping in the Petrov–Galerkin finite element method for convection-diffusion problems
Publication TypeJournal Article
Year of Publication2014
AuthorsSiryk, SV, Salnikov, NN
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2014.05.039
Issue5
SectionInformation Science and Cybernetics
Pagination39-44
Date Published5/2014
LanguageRussian
Abstract

We address the topics of overcoming the dispersive and dissipative effects that arise after the application of mass lumping in the finite-element Petrov–Galerkin method for convection-diffusion problems. A generalization of some earlier results in this field is carried out, as well as the comparison with other existing approaches. The test calculations confirm the theoretical results obtained.

Keywordsconvection-diffusion problems, Petrov–Galerkin finite element method
References: 

1. Finlayson B. A. Numerical methods for problems with moving fronts. Seattle; Washington: Ravenna Park Publ., 1992.
2. Roos H.-G., Stynes M., Tobiska L. Robust numerical methods for singularly perturbed differential equations. Berlin: Springer-Verlag, 2008.
3. Sirik S. V., Salnikov N. N. Probl. upravleniia i informatikli, 2012, No. 1: 94–110 (in Russian).
4. Zienkiewicz O. Z., Taylor R. L. The finite element method. Vol. 1: The basis. Oxford: Butterworth-Heinemann, 2000.
5. Hansbo P. Comput. Methods Appl. Mech. Engrg., 1994, 117: 423–437. https://doi.org/10.1016/0045-7825(94)90127-9
6. Wendland E., Schulz H. E. Revista Minerva., 2005, 2, No. 2: 227–233.
7. Sirik S. V. Kibernetika i system. analiz, 2013, No. 5: 152–163 (in Russian).
8. Guermond J.-L., Pasquetti R. Comput. Methods Appl. Mech. Engrg., 2013, 253: 186–198. https://doi.org/10.1016/j.cma.2012.08.011
9. Samarskiy A. A., Popov Yu. P. Difference Methods solutions Gas-fired dynamics problems. 5th ed. Moscow: Liborkom, 2009 (in Russian).
10. Skvortsov L. M. Vychislit. metody i programmirovanie, 2008, 9: 154–162 (in Russian).