Numerical Methods for Mixed Finite Element Problems: Applications to Incompressible Materials and Contact...

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Jean Deteix Thierno Diop

Numerical Methods for Mixed Finite Element Problems

Applications to Incompressible Materials and Contact Problems

Jean Deteix, Thierno Diop, Michel Fortin

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English

Springer International Publishing AG
25 September 2022

Numerical analysis; Maths for engineers; Mechanics of solids; Algorithms & data structures

Series: Lecture Notes in Mathematics

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.

By: Jean Deteix, Thierno Diop, Michel Fortin
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2022
Volume: 2318
Dimensions: Height: 235mm, Width: 155mm,
Weight: 203g
ISBN: 9783031126154
ISBN 10: 3031126157
Series: Lecture Notes in Mathematics
Pages: 116
Publication Date: 25 September 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for Numerical Methods for Mixed Finite Element Problems: Applications to Incompressible Materials and Contact Problems

“The book provides a very brief summary to mixed finite elements and provides several literature references. The main focus of the book is on the calculation of numerical solutions for mixed finite element problems with the aid of iterative methods with preconditioners. The numerical results are interesting and can inspire researches for further developments.” (Christoph Erath, zbMATH 1530.65002, 2024)