The Mathematical Basis of Finite Element Methods with Applications to Partial Differential Equations: Based on Lectures at an Expository ConferenceCombining 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. |
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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Common terms and phrases
accuracy Anal analysis apply Babuska basis functions bilinear form boundary conditions boundary value problem Bramble-Hilbert lemma Ciarlet Comp computation conforming constant convergence correction indicators cubic curl curved defined degrees of freedom denote derivatives Dirichlet discrete inf-sup condition Dupont elliptic problems energy norm error bound error estimator example finite element approximation finite element method finite element solution Galerkin approximation Galerkin methods generalised given grad gradient H(curl hierarchical Hilbert space inner product interpolant introduce isoparametric L₂ lemma linear elements linear functional Math Mathematics mesh Mitchell and Wait Morton nodes nonconforming Numer obtain optimal parabolic parameter Partial Differential Equations patch test Petrov-Galerkin methods piecewise linear piecewise polynomials points Poisson problem quadratic Raviart refinement satisfies Schatz singular smooth Sobolev spaces Stokes equations Stummel subspace superconvergence technique test functions test space Theorem trial space triangle Wheeler Zienkiewicz