دانلود کتاب روش‌های عددی برای مسائل اجزای محدود مخلوط – کاربردها برای مواد تراکم ناپذیر و مشکلات تماس

Mixed Finite Element Methods are often discarded because they lead to indefinite systems which are more difficult to solve than the nice positive definite problems of standard methods. Indeed, solving indefinite systems is a challenge : direct methods might need renumbering of the equations and standard iterative methods are likely to stagnate or to diverge as proved in. As an example, consider the classical conjugate gradient method. Applied to a symmetric indefinite problem it will generate a diverging sequence. As the conjugate gradient method is (in exact arithmetic) a direct method, it will yield the exact solution if the problem is small enough to avoid loosing orthogonality. Applying a minimum residual method to the same problem will in most cases yield stagnation. These two classical methods are the simplest in a list which grows constantly. This monograph does not intend to introduce new iteration methods. We shall rely mostly on existing packages, mostly Petsc from Argonne Laboratory.