## Adaptive Computational Methods for Partial Differential EquationsList of participants; Elliptic equations; Parabolic equations; Hyperbolic equations. |

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### Contents

Need for Adaptive Methods for Partial Differential Equations Vera F Dunder | 20 |

Adaptive Mesh Refinement and A Posteriori Error Estimation for the pVersion | 33 |

Adaptive Methods and Error Estimation for Elliptic Problems of Structural | 57 |

The Efficient Implementation of Local Mesh Refinement Algorithms | 74 |

The Use of Transfinite Mappings with Finite Elements on a Moving Mesh | 85 |

A Discussion of Some Criteria for the Use of Adaptive Gridding H A Dvvyer | 111 |

A Posteriori Error Estimation and Adaptive Finite Element Grids for Parabolic | 123 |

Adaptive Finite Element Methods for Parabolic Partial Differential Equations | 144 |

Alternate Modes to Control the Nodes in the Moving Finite Element Method | 165 |

Opportunities for Application of Adaptive Grids in Computational Aero | 185 |

Role of Adaptive Grid Techniques in Blast Dynamics | 193 |

Application of Adaptive Grids to Transient Problems Dale A Anderson | 208 |

Adaptive Numerical Methods for Hyperbolic Conservation Laws Ami Harten | 224 |

Data Structures for Adaptive Mesh Refinement Marsha Berger | 237 |

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### Common terms and phrases

accuracy adaptive grid techniques adaptive mesh adaptive mesh refinement adaptive methods algorithm analysis application approach approximate BABUSKA basis functions blast wave boundary conditions boundary layer boundary value calculation clustering computational Conservation Laws convergence correction indicators data structures defined degrees of freedom Department of Mathematics discontinuity discretization discussed dynamic energy norm EPSDN equidistribution example FEMOL finite difference finite element method finite element solution flagged points flow field gradient grid points grid speed hierarchical hyperbolic initial integration interpolation irregular Mach reflection iterative load mesh refinement MILLER nonlinear number of elements numerical analysis numerical solution obtain parabolic partial differential equations Peclet number performance measure piecewise linear post-processing posteriori posteriori error estimates predicted present quadrature region regridding Research scheme Section shock wave shown in Figure solving space Stefan problem strategy tion transfinite mappings two-dimensional U.S. Army University of Maryland velocity viscosity W. C. RHEINBOLDT weighted MFE zero