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Numerical study of the incremental unknowns method
Author(s) -
Garcia Salvador
Publication year - 1994
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690100107
Subject(s) - mathematics , convergence (economics) , aliasing , mathematical optimization , computer science , filter (signal processing) , economics , computer vision , economic growth
Through numerical experiments we explore the incremental unknowns method; linear stationary as well as evolutionary problems are considered. For linear stationary problems, the method appears as a nearly optimal two‐step preconditioning technique. At each step, we observe that the convergence behavior of the iterative methods employed is dramatically different, depending upon whether or not preconditioning is used. For linear evolutionary problems, successful and sharply accurate long‐term integration is observed when the incremental unknowns (other than that of the coarsest level) are, effectively, small quantities. Otherwise, systematical aliasing arises. © 1994 John Wiley & Sons, Inc.