Braess D. Finite elements: Theory, Fast Solvers, and Applications in Solid Mechanics

3rd Edition. — Cambridge University Press, 2007. — 382 p.The method of finite elements is one of the main tools for the numerical treatment of elliptic and parabolic partial differential equations. Because it is based on the variational formulation of the differential equation, it is much more flexible than finite difference methods and finite volume methods, and can thus be applied to more complicated problems. For a long time, the development of finite elements was carried out in parallel by both mathematicians and engineers, without either group acknowledging the other. By the end of the 60’s and the beginning of the 70’s, the material became sufficiently standardized to allow its presentation to students. This book is the result of a series of such lectures.Conforming Finite Elements.
Nonconforming and Other Methods.
The Conjugate Gradient Method.
Multigrid Methods.
Finite Elements in Solid Mechanics.