One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The textas first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimensions. Additional topics include least squares and other Galerkin methods. Many helpful definitions, examples, and exercises appear throughout the book. A classic reference in spline theory, this volume will benefit experts as well as students of engineering and mathematics.a triangulation or a simple isoparametric transform onto an approximation 12 of S2. ... A second and equally serious difficulty arises when we have a third, fourth, or higher order problem to solve over a two- or ... The reason for this lies in the definition of the bilinear form a(u, v) giving rise to the finite element approximate to the given differential equation. ... Irons conjectured that a patch test to determine whether the modified finite element procedure using 5( , ) reproduces polynomial anbsp;...

Title | : | Splines and Variational Methods |

Author | : | P. M. Prenter |

Publisher | : | Courier Corporation - 2013-11-26 |

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