An Analysis of the Finite Element Method |
Contents
AN INTRODUCTION TO THE THEORY | 1 |
A SUMMARY OF THE THEORY | 101 |
APPROXIMATION | 136 |
Copyright | |
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accuracy admissible space algorithm applied basis functions bicubic bilinear bound boundary conditions coefficients computed condition number constant continuous coordinates corresponding cubic derivatives difference equation differential equation dimension Dirichlet Dirichlet problem discrete displacement domain edge eigenfunctions eigenvalue problem elliptic essential boundary essential boundary conditions exactly example finite difference finite element method func Galerkin Hermite inequality inner product interpolate isoparametric linear elements mass matrix midpoint minimizing nodal parameters nodes numerical integration O(h² order h patch test piecewise linear piecewise polynomials polygon positive definite proof quadratic quadrature rate of convergence Rayleigh quotient regular mesh Ritz method roundoff satisfy Section singular functions smooth solution space Sh splines square stiffness matrix strain energy subspace subspace Sh Suppose theorem theory tion trial functions trial space triangles u₁ unknowns values vanish variational vector zero