## Computational Galerkin Methods |

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### Contents

Traditional Galerkin Methods | 1 |

Computational Galerkin Methods | 72 |

Galerkin FiniteElement Methods | 86 |

Copyright | |

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### Common terms and phrases

accuracy algebraic equations applying the Galerkin approximate solution boundary conditions boundary layer Burgers Chebyshev polynomials collocation method Comp convective conventional Galerkin convergence rate cubic derivatives dimension domain eigenvalue error estimates evaluated exact solution example Finite Element Method finite-difference method finite-difference scheme Fletcher flow Fluid Galerkin finite-element method Galerkin formulation Galerkin solution given global governing equation Green's theorem higher-order hyperbolic inner product integration interpolation introduced L2 norm least-squares linear elements matrix methods of weighted Mikhlin Navier-Stokes equations nodal unknowns nodes nondimensional nonlinear terms obtained one-dimensional ordinary differential equations Orszag orthogonal parabolic parameter partial differential equation Petrov-Galerkin formulation problem produces quadratic rectangular elements Reynolds number shape functions shown in Fig shown in Table solution of eq solving spatial spectral method system of equations techniques test and trial test function tions traditional Galerkin method trial functions trial solution two-dimensional typical uniform grid unknown coefficients upwind variation weighted residuals