Nets on a Riemannian manifold and finite-dimensional approximations of the Laplacian
Jacek Komorowski
GDML_Books, (1979), p.

CONTENTSIntroduction......................................................................................................................................... 5Chapter I. Families of nets on a Riemannian manifold............................................................. 8 1. Family of canonical triangulations of Rm...................................................................... 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

EUDML-ID : urn:eudml:doc:268645 
@book{bwmeta1.element.zamlynska-c3f09aa3-adb8-449b-9488-40e6e6274311,
     author = {Jacek Komorowski},
     title = {Nets on a Riemannian manifold and finite-dimensional approximations of the Laplacian},
     series = {GDML\_Books},
     publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
     address = {Warszawa},
     year = {1979},
     zbl = {0422.53022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-c3f09aa3-adb8-449b-9488-40e6e6274311}
}

Jacek Komorowski. Nets on a Riemannian manifold and finite-dimensional approximations of the Laplacian. GDML_Books (1979),  http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-c3f09aa3-adb8-449b-9488-40e6e6274311/