Stable finite element methods with divergence augmentation for the Stokes problem?

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The mixed finite element approximation scheme with divergence augmentation for the Stokes problem is analyzed. We show that the Pk+1 - Pk-1 triangular elements or the Q(k+1) - Q(k-1) quadrilateral elements in R-2, k greater than or equal to 1, are stable with h(k+1/2) convergence in H-1-norm for velocity and h(k) convergence in L-2-norm for pressure. Moreover, h(k+1) convergence in H(div)-norm for velocity can be shown if the domain is convex. In R-3, the cross-grid Pk+1 - Pk-1 tetrahedral elements, k greater than or equal to 2, can be analyzed analogously for the approximation scheme with divergence augmentation and pressure stabilization. A numerical test which confirms the convergence analysis is presented. (C) 2001 Elsevier Science Ltd. All rights reserved.
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Issue Date
2001-04
Language
English
Article Type
Article
Citation

APPLIED MATHEMATICS LETTERS, v.14, no.3, pp.321 - 326

ISSN
0893-9659
URI
http://hdl.handle.net/10203/80391
Appears in Collection
MA-Journal Papers(저널논문)
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