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CONVERGENCE ANALYSIS ON THE GIBOU-MIN METHOD FOR THE HODGE PROJECTION

Title
CONVERGENCE ANALYSIS ON THE GIBOU-MIN METHOD FOR THE HODGE PROJECTION
Authors
Yoon, GangjoonPark, Jea-HyunMin, Chohong
Ewha Authors
민조홍
SCOPUS Author ID
민조홍scopus
Issue Date
2017
Journal Title
COMMUNICATIONS IN MATHEMATICAL SCIENCES
ISSN
1539-6746JCR Link
Citation
vol. 15, no. 5, pp. 1211 - 1220
Keywords
Hodge projectionfinite volume methodPoisson equationGibou-Min
Publisher
INT PRESS BOSTON, INC
Indexed
SCIE; SCOPUS WOS
Abstract
The Hodge projection of a vector field is the divergence-free component of its Helmholtz decomposition. In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. In the decomposition by the Gibou-Min method, an important L-2-orthogonality holds between the gradient field and the solenoidal field, which is similar to the continuous Hodge decomposition. Using the orthogonality, we present a novel analysis which shows that the convergence order is 1.5 in the L-2-norm for approximating the divergence-free vector field. Numerical results are presented to validate our analyses.
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자연과학대학 > 수학전공 > Journal papers
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