## The mathematical basis of finite element methods: with applications to partial differential equationsCombining theoretical insights with practical applications, this stimulating collection provides a state-of-the-art survey of the finite element method, one of the most powerful tools available for the solution of physical problems. Written by leading experts, this volume consider such topics as parabolic Galerkin methods, nonconforming elements, the treatment of singularities in elliptic boundary value problems, and conforming methods for self-adjount elliptic problems. This will be an invaluable basic reference for computational mathematicians and engineers who use finite element methods in academic or industrial research. |

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### Contents

Function spaces by R Wait | 1 |

Conforming methods for selfadjoint elliptic problems by | 15 |

A short survey of parabolic Galerkin methods by T Dupont | 27 |

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accuracy Anal apply Babuska basis functions bilinear form boundary conditions boundary value problem Bramble-Hilbert lemma Ciarlet Comp computation conforming convergence correction indicators cubic curl defined degrees of freedom denote derivatives dimensional Dirichlet discrete inf-sup condition Dupont elliptic problems energy norm error bound error estimator example finite element analysis finite element approximation finite element method finite element solution Galerkin approximation Galerkin methods generalised given grad gradient H ft hierarchical Hilbert space inner product interpolant introduce isoparametric lemma linear elements linear functional Math Mathematics mesh Mitchell and Wait mixed finite element Morton nodes nonconforming Numer obtain optimal parabolic parameter Partial Differential Equations patch test Petrov-Galerkin methods piecewise linear piecewise polynomials points Poisson problem problem 3.1 quadratic Raviart refinement satisfies Schatz singular smooth Sobolev spaces space H Stokes equations Stummel subspace superconvergence technique test functions test space Theorem trial space triangle Wheeler Zienkiewicz