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Hybrid and incompatible finite element methods. (English) Zbl 1110.65003
CRC Series: Modern Mechanics and Mathematics 4. Boca Raton, FL: CRC Press (ISBN 1-58488-276-X/hbk; 978-0-203-48769-3/ebook). xvi, 378 p. (2006).
Publisher’s description: While the theory and application of finite elements methods can be extended to incompatible, hybrid, and mixed element methods, important issues, such as determining the reliability of the solution of incompatible multivariable elements, along with a common perception of impracticality, have hindered the widespread implementation of these methods. Today, however, recent advances – many directly attributable to these authors – have allowed the development of the stability theory and abstract mathematics to useful tools.
The bold introduces these advances in the theory and applications of incompatible and multivariable finite element methods. After an overview of the variation formulation of finite element methods in solid mechanics, the authors discuss the fundamental theory and systematically demonstrate the theoretical foundations of incompatible elements and their application to different problems in the theory of elasticity. They also introduce new ideas in the development of hybrid finite elements, study the numerical stability of the hybrid and mixed element, and establish the theory of zero energy deformation modes. The final chapters, explore applications to fracture problems, present a bound analysis for fracture parameters, and demonstrate an implementation of a finite element analysis program.

MSC:
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
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