Open AccessNumerical integration on higher dimensional simplicial and curved finite elements
Author(s) -
Sergey Korotov,
Michal Křížek
Publication year - 2022
Publication title -
journal of computational mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-8686
DOI - 10.26524/cm135
Subject(s) - monomial , jacobian matrix and determinant , mathematics , tetrahedron , finite element method , numerical integration , degree (music) , mathematical analysis , quadrature (astronomy) , geometry , pure mathematics , physics , acoustics , thermodynamics , optics
We present a formula which evaluates lower degree monomials over higher dimensional simplices by means of integration of higher degree monomials over an interval, triangle or tetrahedron. Further, we show how to apply some higher order quadrature formulae on curved elements using a one-to-one mapping from the reference simplicial element to a curved element.Finally, we demonstrate that the non-zero Jacobian does not imply that this mapping is one-to-one.