## Multilevel Projection Methods for Partial Differential EquationsThe multilevel projection method is a new formalism that provides a framework for the development of multilevel algorithms in a very general setting. This methodology guides the choices of all the major multilevel processes, including relaxation and coarsening, and it applies directly to global or locally-refined discretizations. This book was developed from lectures at the CBMS-NSF Regional Conference on Multigrid and Multilevel Adaptive Methods for Partial Differential Equations in June 1991, and is a supplement to Multilevel Adaptive Methods for Partial Differential Equations, also written by Stephen F. McCormick. |

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### Contents

CB62_ch1 | 1 |

CB62_ch2 | 31 |

CB62_ch3 | 49 |

CB62_ch4 | 61 |

CB62_ch5 | 97 |

CB62_appendixa | 103 |

CB62_appendixb | 107 |

CB62_appendixc | 110 |

111 | |

### Other editions - View all

Multilevel Projection Methods for Partial Differential Equations Stephen F. McCormick Limited preview - 1992 |

Multilevel Projection Methods for Partial Differential Equations Stephen F. McCormick No preview available - 1992 |

Multilevel Projection Methods for Partial Differential Equations Stephen F. McCormick No preview available - 1992 |

### Common terms and phrases

actual error AFAC algebraic error algorithm applied approximation arrays assume basic bilinear bilinear interpolation cells coarse-grid correction coarse-level coarsening process components composite grid computational continuum function corresponding cycle defined developed dimension Dirichlet Dirichlet boundary conditions discretization error eigenvalue problem equation error measures estimate Euclidean norm Euclidean space example fine-grid finite element functions Galerkin given global grid grid 2h grid point inner product iteration Kaczmarz kcyc Kh(wh L2 norm level h Lhuh linear prototype matrix McCormick monograph multigrid method multilevel methods multilevel projection method nodal vector nonlinear null space operator parameter performance piecewise point Gauss–Seidel Pran prototype problems Psan v2h realizability refinement relaxation scheme residual error norm Rh(uh Rh(wh set uh solution Solve solver subroutine subspaces uniform grid unigrid V-cycle variational form w?h e S2h wh-i whe Sh whº zero