Generalizations of the Finite Element Method
Open Mathematics (2012)
- Volume: 10, Issue: 1, page 3-24
- ISSN: 2391-5455
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topMarc Schweitzer. "Generalizations of the Finite Element Method." Open Mathematics 10.1 (2012): 3-24. <http://eudml.org/doc/269166>.
@article{MarcSchweitzer2012,
abstract = {This paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method. We review these approaches and interpret them in the more general framework of the partition of unity method. Here we focus on fundamental construction principles, approximation properties and stability of the respective numerical method. To this end, we consider meshbased and meshfree generalizations of the finite element method and the use of smooth, discontinuous, singular and numerical enrichment functions.},
author = {Marc Schweitzer},
journal = {Open Mathematics},
keywords = {Generalized Finite Element Method; Extended Finite Element Method; Partition of Unity Method; generalized finite element method; extended finite element method; partition of unity method; stability; meshfree generalizations},
language = {eng},
number = {1},
pages = {3-24},
title = {Generalizations of the Finite Element Method},
url = {http://eudml.org/doc/269166},
volume = {10},
year = {2012},
}
TY - JOUR
AU - Marc Schweitzer
TI - Generalizations of the Finite Element Method
JO - Open Mathematics
PY - 2012
VL - 10
IS - 1
SP - 3
EP - 24
AB - This paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method. We review these approaches and interpret them in the more general framework of the partition of unity method. Here we focus on fundamental construction principles, approximation properties and stability of the respective numerical method. To this end, we consider meshbased and meshfree generalizations of the finite element method and the use of smooth, discontinuous, singular and numerical enrichment functions.
LA - eng
KW - Generalized Finite Element Method; Extended Finite Element Method; Partition of Unity Method; generalized finite element method; extended finite element method; partition of unity method; stability; meshfree generalizations
UR - http://eudml.org/doc/269166
ER -
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