Journal
IMA JOURNAL OF NUMERICAL ANALYSIS
Volume 33, Issue 3, Pages 974-1007Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imanum/drs023
Keywords
Finite Elements; Stabilized Methods; High Order Approximation
Categories
Funding
- Spanish Government [MTM 2009-07719]
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In this paper, we introduce a low-cost, high-order stabilized method for the numerical solution of incompressible flow problems. This is a particular type of projection-stabilized method where each targeted operator, such as the pressure gradient or the convection, is stabilized by least-squares terms added to the Galerkin formulation. The main methodological originality is that we replace the projection-stabilized structure by an interpolation-stabilized structure, with reduced computational cost for some choices of the interpolation operator. This stabilization has one level, in the sense that it is defined on a single mesh. We prove the stability of our formulation by means of a specific inf-sup condition, which is the main technical innovation of our paper. We perform a convergence and error estimates analysis, proving the optimal order of accuracy of our method. We include some numerical tests that confirm our theoretical expectations.
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