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A variational inequality approach to free surface seepage in an inhomogeneous dam
Author(s) -
Westbrook D. R.,
Gilmour Grant J.
Publication year - 1985
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610090608
Subject(s) - finite element method , convergence (economics) , variational inequality , mathematics , projection (relational algebra) , stiffness matrix , surface (topology) , transformation (genetics) , stiffness , matrix (chemical analysis) , symbolic convergence theory , projection method , mathematical analysis , mathematical optimization , geometry , computer science , algorithm , structural engineering , dykstra's projection algorithm , engineering , computer security , economic growth , chemistry , key (lock) , composite material , biochemistry , economics , gene , materials science
The current work uses Baiocchi's transformation to obtain heuristically a formulation of the inhomogeneous dam problem. When finite element methods are applied the finite dimensional problem is a variational inequality which may be solved to obtain approximate solutions. The main advantage of the method is that it uses a fixed mesh. The finite dimensional problem is solved by means of succesive overrelaxation with projection. Although the standard convergence theory 1 for this method does not apply in this case, because the stiffness matrix is not symmetric, satisfactory and rapid convergence was obtained in all of our examples. Numerical results are given for some examples.