# Inner products in covolume and mimetic methods

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

- Volume: 42, Issue: 6, page 941-959
- ISSN: 0764-583X

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topTrapp, Kathryn A.. "Inner products in covolume and mimetic methods." ESAIM: Mathematical Modelling and Numerical Analysis 42.6 (2008): 941-959. <http://eudml.org/doc/250375>.

@article{Trapp2008,

abstract = {
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.
},

author = {Trapp, Kathryn A.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Compatible discretization; discrete Helmholtz orthogonality; discrete exact sequence; mimetic method; covolume method.; compatible discretization; covolume method; finite element methods},

language = {eng},

month = {7},

number = {6},

pages = {941-959},

publisher = {EDP Sciences},

title = {Inner products in covolume and mimetic methods},

url = {http://eudml.org/doc/250375},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Trapp, Kathryn A.

TI - Inner products in covolume and mimetic methods

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2008/7//

PB - EDP Sciences

VL - 42

IS - 6

SP - 941

EP - 959

AB -
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.

LA - eng

KW - Compatible discretization; discrete Helmholtz orthogonality; discrete exact sequence; mimetic method; covolume method.; compatible discretization; covolume method; finite element methods

UR - http://eudml.org/doc/250375

ER -

## References

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