Geometric decompositions and local bases for spaces of finite element differential forms Export

@article{citeulike:3883225, abstract = {We study the two primary families of spaces of finite element differential forms with respect to a simplicial mesh in any number of space dimensions. These spaces are generalizations of the classical finite element spaces for vector fields, frequently referred to as Raviart\&\#x2013;Thomas, Brezzi\&\#x2013;Douglas\&\#x2013;Marini, and N\&\#xe9;d\&\#xe9;lec spaces. In the present paper, we derive geometric decompositions of these spaces which lead directly to explicit local bases for them, generalizing the Bernstein basis for ordinary Lagrange finite elements. The approach applies to both families of finite element spaces, for arbitrary polynomial degree, arbitrary order of the differential forms, and an arbitrary simplicial triangulation in any number of space dimensions. A prominent role in the construction is played by the notion of a consistent family of extension operators, which expresses in an abstract framework a sufficient condition for deriving a geometric decomposition of a finite element space leading to a local basis.}, author = {Arnold, D. and Falk, R. and Winther, R.}, citeulike-article-id = {3883225}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.cma.2008.12.017}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0045782509000048}, day = {08}, doi = {10.1016/j.cma.2008.12.017}, issn = {00457825}, journal = {Computer Methods in Applied Mechanics and Engineering}, keywords = {finite-elements}, month = {January}, posted-at = {2009-01-16 15:30:57}, priority = {2}, title = {Geometric decompositions and local bases for spaces of finite element differential forms}, url = {http://dx.doi.org/10.1016/j.cma.2008.12.017}, year = {2009} }

TY - JOUR ID - citeulike:3883225 L3 - citeulike-article-id:3883225 N2 - We study the two primary families of spaces of finite element differential forms with respect to a simplicial mesh in any number of space dimensions. These spaces are generalizations of the classical finite element spaces for vector fields, frequently referred to as Raviart–Thomas, Brezzi–Douglas–Marini, and Nédélec spaces. In the present paper, we derive geometric decompositions of these spaces which lead directly to explicit local bases for them, generalizing the Bernstein basis for ordinary Lagrange finite elements. The approach applies to both families of finite element spaces, for arbitrary polynomial degree, arbitrary order of the differential forms, and an arbitrary simplicial triangulation in any number of space dimensions. A prominent role in the construction is played by the notion of a consistent family of extension operators, which expresses in an abstract framework a sufficient condition for deriving a geometric decomposition of a finite element space leading to a local basis. JF - Computer Methods in Applied Mechanics and Engineering SN - 00457825 TI - Geometric decompositions and local bases for spaces of finite element differential forms KW - finite-elements AU - Arnold, D AU - Falk, R AU - Winther, R PY - 2009/01/08/ UR - http://dx.doi.org/10.1016/j.cma.2008.12.017 ER -