## Finite difference methods on irregular networks: a generalized approach to second order elliptic problems |

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### Contents

CONSTRUCTION OF FINITE DIFFERENCE APPROXIMATIONS | 40 |

ERROR ESTIMATES AND CONVERGENCE | 96 |

FINITE DIFFERENCE SCHEMES FOR N0NSYMMETRIC PROBLEMS | 150 |

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### Common terms and phrases

affine transformation angles Appendix EX approximation error asymptotic behaviour balance equations boundary conditions bounds Bramble-Hilbert Lemma C-norm coefficients considered convergence convergent boundary cubature defined denote depend derived difference operators difference quotients discrete analogues domain elliptic error estimates error functional estimation regions FDM via balance FDSs A^y fh(x finite element fulfilled Furthermore Green's formula grid functions grid points grid regularity condition HEINRICH inequalities kh(x KVu,n)ds Lg-norms line integral linear locally irregular networks matrix MD-schemes mesh segment method MD method PB midpoint mixed boundary conditions monograph Moreover networks of triangles norms PB-schemes polygonal positive definiteness priori estimates Proof proved rectangles Remark rhombus right-hand side satisfied scalar product secondary networks Section seminorms smoothness assumptions Sobolev spaces solution subsets sufficiently small hQ symmetry take into account taken Taylor's expansion Theorem 3.1 tion trace theorems transformation upwind triangles vector xeco

### References to this book

Nonlinear Functional Analysis and Its Applications: Part 2 B: Nonlinear ... E. Zeidler No preview available - 1989 |

Multilevel Adaptive Methods for Partial Differential Equations Stephen F. McCormick No preview available - 1989 |