## The finite element method and its applications |

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### Contents

THE BASIC IDEA OF THE FINITE ELEMENT | 1 |

THE VARIATIONAL PRINCIPLE | 9 |

3 ERROR ANALYSIS OF THE FINITE ELEMENT | 24 |

Copyright | |

3 other sections not shown

### Common terms and phrases

admissible function apply the FEM approximate solution assume basis functions becomes bilinear form boundary dG boundary value problem computation consider constant constraint convection term coordinates defined diagonal differential equation Dirichlet boundary condition domain G dual variational problem dx dy eigenvalue elliptic energy norm error estimate Euler's equation exact solution example finite element method finite element solution free boundary func given heat equation Hilbert space holds inner product interpolate iterative left-hand side linear equations lumped mass system mass matrix maximum principle midpoint minimized minimum variational problem multiply both sides Navier-Stokes equation numerical integration obtain ondG piecewise linear basis piecewise linear polynomials positive definite quadratic respectively right-hand side satisfies scheme seminorm shape functions shown in Fig solve space dimension Stefan problem subspace substitute system of equations system of linear tion transformation trial function triangular element upwind finite element vanishes vector weak form corresponding zero