Numerical methods for mixed finite element problems, applications to incompressible materials and contact problems
Deteix, Jean
Numerical methods for mixed finite element problems : applications to incompressible materials and contact problems [Documento eletrónico] / by Jean Deteix, Thierno Diop, Michel Fortin. - Cham : Springer International Publishing : Springer , 2022 . - VI, 116 p. : il.. - (Lecture Notes in Mathematics) ; 2318 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.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-031-12616-1
Mathematics
Algorithms
Engineering mathematics
Engineering
Numerical analysis
Mechanics, Applied
Solids
LCC QA71-90
Numerical methods for mixed finite element problems : applications to incompressible materials and contact problems [Documento eletrónico] / by Jean Deteix, Thierno Diop, Michel Fortin. - Cham : Springer International Publishing : Springer , 2022 . - VI, 116 p. : il.. - (Lecture Notes in Mathematics) ; 2318 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.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-031-12616-1
Mathematics
Algorithms
Engineering mathematics
Engineering
Numerical analysis
Mechanics, Applied
Solids
LCC QA71-90
