## Approximation on a Rectangular Grid: With Application to Finite Element Methods and Other Problems |

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### Contents

CHAPTER | 1 |

5 The Necessity of the Fundamental Completeness Conditions | 32 |

7 Primitive Systems of Higher Dimensions with Zero Degree | 39 |

Copyright | |

10 other sections not shown

### Other editions - View all

Approximation on a rectangular grid: with application to finite element ... S.G. Mikhlin No preview available - 2011 |

### Common terms and phrases

addition analogous apply approximate solution arbitrary assume boundary conditions boundary value problem bounded calculation Chapter coefficients Consequently consider const constants construct contained continuous converges coordinate functions corresponding cube defined denote derive determinant difference differential dominated easily eigenvalue elements energy equal equation error estimate evaluate exact examine example exist expression extended fact Finally follows formula fundamental completeness conditions given grid Hence holds identity independent inequality integral interval introduce larger linear lower matrix Mikhlin necessary norm obtain Obviously one-dimensional operator ostsi polynomials positive definite present primitive functions primitive system problem prove remains replace respect satisfy sequence situation space square studied subspace sufficiently small takes the form THEOREM values vanish variables variational-difference method vector vertices yields zero