## Analysis of a finite element method--PDE/PROTRAN |

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### Contents

Partial Differential Equation Applications | 1 |

Elliptic ProblemsForming the Algebraic Equations | 22 |

Elliptic ProblemsSolving the Algebraic Equations | 50 |

Copyright | |

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### Common terms and phrases

A.UX algorithm approximating arc number assumed backward difference method band solver basis functions boundary arc boundary conditions calculated components conjugate gradient conjugate gradient method convergence Crank-Nicolson cubic curved D3EST Default defined in GLOBAL derivatives diagonal dimensional discretization error DISPLACEMENTS DOUBLE PRECISION Structure ds R 3R2 dxdy eigenfunction eigenvalue problem evaluated Expression involving constants extrapolation F.UX Figure filename finite difference method finite element method FORTRAN frontal method frontal solver Galerkin Gaussian elimination given grid hyperbolic problems iarcI initial triangulation INTEGER Structure integration inverse power method isoparametric Jacobian matrix keyword Lanczos iters Lanczos method linear system Newton iteration Newton's method node number nonlinear nonzero normalized triangle NOUPDATE nset OUTFREQUENCY output PDE/PROTRAN PDE2D piecewise polynomial plot positive definite quadratic quartic elements REAL or DOUBLE satisfies Section shown solve specified step symmetric TWODEPEP Type unknowns updated UPRINT variables defined vector velocity VERTICES XGRID zero