MATHEMATICAL THEORY OF FINITE ELEMENT METHODS, THE

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. The third edition contains four new sections: the BDDC domain decomposition preconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincare-Friedrichs inequalities for piecewise W[subscript p superscript 1] functions. New exercises have also been added throughout. The initial chapter provides an introduction to the entire subject, developed in the one-dimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequent chapters provide an introduction to: multigrid methods and domain decomposition methods, mixed methods with applications to elasticity and fluid mechanics, iterated penalty and augmented Lagrangian methods, variational "crimes" including nonconforming and isoparametric methods, numerical integration and interior penalty methods, error estimates in the maximum norm with applications to nonlinear problems, error estimators, adaptive meshes and convergence analysis of an adaptive algorithm, Banach-space operator-interpolation techniques.