Inner products in covolume and mimetic methods
Trapp, Kathryn A.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008), p. 941-959 / Harvested from Numdam
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A class of compatible spatial discretizations for solving partial differential equations is presented. A discrete exact sequence framework is developed to classify these methods which include the mimetic and the covolume methods as well as certain low-order finite element methods. This construction ensures discrete analogs of the differential operators that satisfy the identities and theorems of vector calculus, in particular a Helmholtz decomposition theorem for the discrete function spaces. This paper demonstrates that these methods differ only in their choice of discrete inner product. Finally, certain uniqueness results for the covolume inner product are shown.

Publié le : 2008-01-01
DOI : https://doi.org/10.1051/m2an:2008030
Classification:  65N06 
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     author = {Trapp, Kathryn A.},
     title = {Inner products in covolume and mimetic methods},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {42},
     year = {2008},
     pages = {941-959},
     doi = {10.1051/m2an:2008030},
     mrnumber = {2473315},
     zbl = {1155.65103},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2008__42_6_941_0}
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Trapp, Kathryn A. Inner products in covolume and mimetic methods. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008) pp. 941-959. doi : 10.1051/m2an:2008030. http://gdmltest.u-ga.fr/item/M2AN_2008__42_6_941_0/

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