Inner products in covolume and mimetic methods

Kathryn A. Trapp

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

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

Abstract

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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.

How to cite

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Trapp, 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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