Synopses & Reviews
This classic work, on the numerical solution of boundary value problems by variational methods with special emphasis on the finite element and collocation methods, is now available in an unabridged paperback edition. Assuming only the elements of linear algebra and analysis, Prenter presents just the necessary Hilbert space theory and abstract functional analytic concepts before developing the use of splines as a fine approximating tool. This work remains one of the clearest introductions to variational methods and includes powerful applications of approximation theoretic notions to very applied problems.
Table of Contents
Partial table of contents:
INTRODUCTORY IDEAS.
Linear Spaces.
LAGRANGIAN INTERPOLATES.
On Polynomials.
Best Approximation and Extended Error Estimates.
HERMITIAN INTERPOLATES.
Computation of Piecewise Cubic Hermites.
The Hermite-Birkhoff Interpolation Problem.
POLYNOMIAL SPLINES AND GENERALIZATIONS.
APPROXIMATING FUNCTIONS OF SEVERAL VARIABLES.
Surface Fitting.
Tensor Products.
FUNDAMENTALS FOR VARIATIONAL METHODS.
Linear Operators.
Norms, Convergence and Completeness.
THE FINITE ELEMENT METHOD.
Applications to the Dirichlet Problem.
Coerciveness and Rates of Convergence.
Curved Boundaries and Nonconforming Elements.
THE METHOD OF COLLOCATION.
Glossary of Symbols.
Index.