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CONVERGENCE ANALYSIS ON THE GIBOU-MIN METHOD FOR THE HODGE PROJECTION
- CONVERGENCE ANALYSIS ON THE GIBOU-MIN METHOD FOR THE HODGE PROJECTION
- Yoon, Gangjoon; Park, Jea-Hyun; Min, Chohong
- Ewha Authors
- SCOPUS Author ID
- Issue Date
- Journal Title
- COMMUNICATIONS IN MATHEMATICAL SCIENCES
- vol. 15, no. 5, pp. 1211 - 1220
- Hodge projection; finite volume method; Poisson equation; Gibou-Min
- INT PRESS BOSTON, INC
- SCIE; SCOPUS
- 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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