Open Access
2008 Bubble-Enriched Least-Squares Finite Element Method for Transient Advective Transport
Rajeev Kumar, Brian H. Dennis
Differ. Equ. Nonlinear Mech. 2008: 1-21 (2008). DOI: 10.1155/2008/267454


The least-squares finite element method (LSFEM) has received increasing attention in recent years due to advantages over the Galerkin finite element method (GFEM). The method leads to a minimization problem in the L2-norm and thus results in a symmetric and positive definite matrix, even for first-order differential equations. In addition, the method contains an implicit streamline upwinding mechanism that prevents the appearance of oscillations that are characteristic of the Galerkin method. Thus, the least-squares approach does not require explicit stabilization and the associated stabilization parameters required by the Galerkin method. A new approach, the bubble enriched least-squares finite element method (BELSFEM), is presented and compared with the classical LSFEM. The BELSFEM requires a space-time element formulation and employs bubble functions in space and time to increase the accuracy of the finite element solution without degrading computational performance. We apply the BELSFEM and classical least-squares finite element methods to benchmark problems for 1D and 2D linear transport. The accuracy and performance are compared.


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Rajeev Kumar. Brian H. Dennis. "Bubble-Enriched Least-Squares Finite Element Method for Transient Advective Transport." Differ. Equ. Nonlinear Mech. 2008 1 - 21, 2008.


Received: 4 March 2008; Revised: 9 July 2008; Accepted: 5 September 2008; Published: 2008
First available in Project Euclid: 26 January 2017

zbMATH: 1163.65068
MathSciNet: MR2461755
Digital Object Identifier: 10.1155/2008/267454

Rights: Copyright © 2008 Hindawi

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