This book focuses on iterative solvers and preconditioners for
mixed finite element methods. It provides an overview of some of
the state-of-the-art solvers for discrete systems with constraints
such as those which arise from mixed formulations. Starting by
recalling the basic theory of mixed finite element methods, the
book goes on to discuss the augmented Lagrangian method and gives a
summary of the standard iterative methods, describing their usage
for mixed methods. Here, preconditioners are built from an
approximate factorisation of the mixed system. A first set of
applications is considered for incompressible elasticity problems
and flow problems, including non-linear models. An account of the
mixed formulation for Dirichlet's boundary conditions is then given
before turning to contact problems, where contact between
incompressible bodies leads to problems with two constraints. This
book is aimed at graduate students and researchers in the field of
numerical methods and scientific computing.
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