Nets on a Riemannian manifold and finite-dimensional approximations of the Laplacian

Jacek Komorowski. Nets on a Riemannian manifold and finite-dimensional approximations of the Laplacian. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1979. <http://eudml.org/doc/268645>.

@book{JacekKomorowski1979,
abstract = {CONTENTSIntroduction......................................................................................................................................... 5Chapter I. Families of nets on a Riemannian manifold............................................................. 8 1. Family of canonical triangulations of $R^m$...................................................................... 8 2. Non-degeneracy in the case of nets defined by simplicial subdivisions...................... 9 3. Auxiliary lemmas....................................................................................................................... 13 4. Proofs of the auxiliary lemmas............................................................................................... 14 5. Nets defined by successive simplicial and standard geodesic subdivisions............. 18 6. Non-degeneracy in the case of nets defined by standard geodesic subdivisions...... 25Chapter II. Finite-dimensional approximation of the Laplacian................................................ 44 7. Difference forms on a net........................................................................................................ 44 8. Integration. The Stokes theorem........................................................................................... 48 9. Discrete Laplacians on a Riemannian net. The Hodge theorem................................... 52 10. Orientation and Hodge operators on a Riemannian net................................................ 54 11. Approximation of the operator d........................................................................................... 57 12. Approximation of the operator ∂ and the Laplacian......................................................... 64 13. Convergence of the approximations................................................................................... 70References......................................................................................................................................... 79},
author = {Jacek Komorowski},
keywords = {differential operators; Hodge theorem; harmonic forms; triangulation; Laplacian; approximation},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Nets on a Riemannian manifold and finite-dimensional approximations of the Laplacian},
url = {http://eudml.org/doc/268645},
year = {1979},
}

TY - BOOK
AU - Jacek Komorowski
TI - Nets on a Riemannian manifold and finite-dimensional approximations of the Laplacian
PY - 1979
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction......................................................................................................................................... 5Chapter I. Families of nets on a Riemannian manifold............................................................. 8 1. Family of canonical triangulations of $R^m$...................................................................... 8 2. Non-degeneracy in the case of nets defined by simplicial subdivisions...................... 9 3. Auxiliary lemmas....................................................................................................................... 13 4. Proofs of the auxiliary lemmas............................................................................................... 14 5. Nets defined by successive simplicial and standard geodesic subdivisions............. 18 6. Non-degeneracy in the case of nets defined by standard geodesic subdivisions...... 25Chapter II. Finite-dimensional approximation of the Laplacian................................................ 44 7. Difference forms on a net........................................................................................................ 44 8. Integration. The Stokes theorem........................................................................................... 48 9. Discrete Laplacians on a Riemannian net. The Hodge theorem................................... 52 10. Orientation and Hodge operators on a Riemannian net................................................ 54 11. Approximation of the operator d........................................................................................... 57 12. Approximation of the operator ∂ and the Laplacian......................................................... 64 13. Convergence of the approximations................................................................................... 70References......................................................................................................................................... 79
LA - eng
KW - differential operators; Hodge theorem; harmonic forms; triangulation; Laplacian; approximation
UR - http://eudml.org/doc/268645
ER -