| This thesis deals with the condition numbers and singular value distribution of the preconditioned operators ;Three nonconforming finite element methods are being considered. The first two methods, the penalty method and the method of "nearly-zero" boundary conditions, deal with Dirichlet boundary conditions on curved domains. It is shown that if the leading part of A is a smooth function times the leading part of B and if the boundary condition of B is the same as that of A, then the ;The third method uses the ;Through these three particular examples, one has learned what difficulties to anticipate when dealing with nonconforming finite element methods in general. This knowledge is useful when one wishes to derive similar preconditioning results for other nonconforming methods. |
