Higher-order finite element methods /

The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasin...

Full description

Bibliographic Details
Main Author:	Šolin, Pavel
Corporate Author:	Taylor & Francis
Other Authors:	Segeth, Karel, Doležel, Ivo
Format:	eBook
Language:	English
Published:	Boca Raton, FL : Chapman & Hall/CRC, ©2004.
Series:	Studies in advanced mathematics.
Subjects:	Finite element method. Méthode des éléments finis. TECHNOLOGY & ENGINEERING > Engineering (General) TECHNOLOGY & ENGINEERING > Reference. Finite element method Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

INTRODUCTION ; Finite Elements; Orthogonal Polynomials; A One-Dimensional Example; HIERARCHIC MASTER ELEMENTS OF ARBITRARY ORDER ; De Rham Diagram H 1-Conforming Approximations; H (curl)-Conforming Approximations; H (div)-Conforming Approximations; L 2-Conforming Approximations; HIGHER-ORDER FINITE ELEMENT DISCRETIZATION ; Projection-Based Interpolation on Reference Domains; Transfinite Interpolation Revisited; Construction of Reference Maps; Projection-Based Interpolation on Physical Mesh Elements; Technology of Discretization in Two and Three Dimensions; Constrained Approximation; Selected Software-Technical Aspects; HIGHER-ORDER NUMERICAL QUADRATURE ; One-Dimensional Reference Domain K(a) ; Reference Quadrilateral K(q) ; Reference Triangle K(t) ; Reference Brick K(B) ; Reference Tetrahedron K(T) ; Reference Prism K(P) ; NUMERICAL SOLUTION OF FINITE ELEMENT EQUATIONS ; Direct Methods for Linear Algebraic Equations; Iterative Methods for Linear Algebraic Equations; Choice of the Method; Solving Initial Value Problems for ordinary Differential Equations; MESH OPTIMIZATION, REFERENCE SOLUTIONS, AND hp- ADAPTIVITY ; Automatic Mesh Optimization in One Dimension; Adaptive Strategies Based on Automatic Mesh Optimization; Goal-Oriented Adaptivity; Automatic Goal-Oriented h-, p-, and hp- Adaptivity; Automatic Goal-Oriented hp -Adaptivity in Two Dimensions