Mixed methods on quadrilaterals and hexahedra

Autor:	Philip T. Keenan
Rok vydání:	1994
Předmět:	Discrete mathematics Pure mathematics Partial differential equation Quadrilateral Differential geometry Applied Mathematics Bilinear transform Polygon mesh Mixed finite element method Hexahedron Finite element method Mathematics::Numerical Analysis Mathematics
Zdroj:	Numerical Algorithms. 7:269-293
ISSN:	1572-9265 1017-1398
DOI:	10.1007/bf02140687
Popis:	We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::434a5cee7b4bb2c40ed048971569dae0 https://doi.org/10.1007/bf02140687 Zobrazit plný text záznamu Full text from SpringerLink